Chapter 15 Debt and Taxes


 Sabina Floyd
 1 years ago
 Views:
Transcription
1 hapter 15 Debt and Taxes Pelamed Pharmaceutcals has EBIT of $325 mllon n In addton, Pelamed has nterest expenses of $125 mllon and a corporate tax rate of 40%. a. What s Pelamed s 2006 net ncome? b. What s the total of Pelamed s 2006 net ncome and nterest payments? c. If Pelamed had no nterest expenses, what would ts 2006 net ncome be? How does t compare to your answer n part (b)? d. What s the amount of Pelamed s nterest tax sheld n 2006? a. Net Income = EBIT Interest Taxes = ( ) ( 0.40 ) = $120 mllon. b. Net ncome + Interest = = $245 mllon c. Net ncome = EBIT Taxes = 325 ( 0.40 ) = $195 mllon. Ths s = $50 mllon lower than part (b). d. Interest tax sheld = % = $50 mllon Grommt Engneerng expects to have net ncome next year of $20.75 mllon and free cash flow of $22.15 mllon. Grommt s margnal corporate tax rate s 35%. a. If Grommt ncreases leverage so that ts nterest expense rses by $1 mllon, how wll ts net ncome change? b. For the same ncrease n nterest expense, how wll free cash flow change? a. Net ncome wll fall by the aftertax nterest expense to $ ( 0.35 ) = $20. mllon. b. Free cash flow s not affected by nterest expenses Suppose the corporate tax rate s 40%. onsder a frm that earns $00 before nterest and taxes each year wth no rsk. The frm s captal expendtures equal ts deprecaton expenses each year, and t wll have no changes to ts net workng captal. The rskfree nterest rate s 5%. a. Suppose the frm has no debt and pays out ts net ncome as a dvdend each year. What s the value of the frm s equty? b. Suppose nstead the frm makes nterest payments of $500 per year. What s the value of equty? What s the value of debt? c. What s the dfference between the total value of the frm wth leverage and wthout leverage? d. The dfference n part (c) s equal to what percentage of the value of the debt?
2 194 Berk/DeMarzo orporate Fnance, Second Edton a. Net ncome = 00 ( 40% ) = $600. Thus, equty holders receve dvdends of $600 per year wth no rsk. 600 E = = $12, 000 5% 300 b. Net ncome = ( ) ( 0.40 ) = $300 E = = $6000. Debt holders receve nterest 5% of $500 per year D = $,000 c. Wth leverage = 6,000 +,000 = $16,000 Wthout leverage = $12,000 Dfference = 16,000 12,000 = $4000 4,000 d. = 40% = corporate tax rate, Braxton Enterprses currently has debt outstandng of $35 mllon and an nterest rate of 8%. Braxton plans to reduce ts debt by repayng $7 mllon n prncpal at the end of each year for the next fve years. If Braxton s margnal corporate tax rate s 40%, what s the nterest tax sheld from Braxton s debt n each of the next fve years? Year Debt Interest Tax Sheld Your frm currently has $0 mllon n debt outstandng wth a % nterest rate. The terms of the loan requre the frm to repay $25 mllon of the balance each year. Suppose that the margnal corporate tax rate s 40%, and that the nterest tax shelds have the same rsk as the loan. What s the present value of the nterest tax shelds from ths debt? Year Debt Interest Tax Sheld PV $ Arnell Industres has just ssued $ mllon n debt (at par). The frm wll pay nterest only on ths debt. Arnell s margnal tax rate s expected to be 35% for the foreseeable future. a. Suppose Arnell pays nterest of 6% per year on ts debt. What s ts annual nterest tax sheld? b. What s the present value of the nterest tax sheld, assumng ts rsk s the same as the loan? c. Suppose nstead that the nterest rate on the debt s 5%. What s the present value of the nterest tax sheld n ths case? a. Interest tax sheld = $ 6% 35% = $0.21 mllon b. $0.21 PV(Interest tax sheld) = = $3.5 mllon 0.06
3 Berk/DeMarzo orporate Fnance, Second Edton 195 c. Interest tax sheld = $ 5% 35% = $0.175 mllon. $0.175 PV = = $3.5 mllon Ten years have passed snce Arnell ssued $ mllon n perpetual nterest only debt wth a 6% annual coupon, as n Problem 6. Tax rates have remaned the same at 35% but nterest rates have dropped so Arnell s current cost of debt captal s 4%. a. What s Arnell s annual nterest tax sheld? b. What s the present value of the nterest tax sheld today? a. Soluton Interest tax sheld = $ 6% 35% = $0.21 mllon $0.21 b. Soluton PV(Interest tax sheld) = = $5.25 mllon Alternatvely, new market value of debt s D = (.06)/.04 = $15 mllon. Tc D = 35% 15 = $5.25 mllon Bay Transport Systems (BTS) currently has $30 mllon n debt outstandng. In addton to 6.5% nterest, t plans to repay 5% of the remanng balance each year. If BTS has a margnal corporate tax rate of 40%, and f the nterest tax shelds have the same rsk as the loan, what s the present value of the nterest tax sheld from the debt? Interest tax sheld n year 1 = $30 6.5% 40% = $0.78 mllon. As the outstandng balance declnes, so wll the nterest tax sheld. Therefore, we can value the nterest tax sheld as a growng perpetuty wth a growth rate of g = 5% and r = 6.5%: $0.78 PV = = $6.78 mllon 6.5% + 5% Safeco Inc. has no debt, and mantans a polcy of holdng $ mllon n excess cash reserves, nvested n rskfree Treasury securtes. If Safeco pays a corporate tax rate of 35%, what s the cost of permanently mantanng ths $ mllon reserve? (Hnt: what s the present value of the addtonal taxes that Safeco wll pay?) D = $ mllon (negatve debt) So PV(Interest tax sheld) = Tc D = $3.5 mllon. Ths s the present value of the future taxes Safeco wll pay on the nterest earned on ts reserves Rogot Instruments makes fne Volns and ellos. It has $1 mllon n debt outstandng, equty valued at $2 mllon, and pays corporate ncome tax at rate 35%. Its cost of equty s 12% and ts cost of debt s 7%. a. What s Rogot s pretax WA? b. What s Rogot s (effectve aftertax) WA? E D 2 1 = r + r (1 ) = =.33% E + D E + D 3 3 a. rwacc E D τ c E D 2 1 = r + r (1 ) = 12+ 7(.65) = 9.52% E + D E + D 3 3 b. rwacc E D τ c
4 196 Berk/DeMarzo orporate Fnance, Second Edton Rumolt Motors has 30 mllon shares outstandng wth a prce of $15 per share. In addton, Rumolt has ssued bonds wth a total current market value of $150 mllon. Suppose Rumolt s equty cost of captal s %, and ts debt cost of captal s 5%. a. What s Rumolt s pretax weghted average cost of captal? b. If Rumolt s corporate tax rate s 35%, what s ts aftertax weghted average cost of captal? a. E = $15 30 = $450 mllon. D = $150 mllon. Pretax WA = % + 5% = 8.75% WA = % + 5% 35% = % b. ( ) Summt Bulders has a market debtequty rato of 0.65 and a corporate tax rate of 40%, and t pays 7% nterest on ts debt. The nterest tax sheld from ts debt lowers Summt s WA by what amount? D E+ D = 1.65 =. Therefore, WA = Pretax WA.394(7%)(.40) = Pretax WA 1.% So, t lowers t by 1.1% NatNah, a bulder of acoustc accessores, has no debt and an equty cost of captal of 15%. Suppose NatNah decdes to ncrease ts leverage and mantan a market debttovalue rato of 0.5. Suppose ts debt cost of captal s 9% and ts corporate tax rate s 35%. If NatNah s pretax WA remans constant, what wll ts (effectve aftertax) WA be wth the ncrease n leverage? D rd Pretax Wacc 15% % E+ D τ = = Restex mantans a debtequty rato of 0.85, and has an equty cost of captal of 12% and a debt cost of captal of 7%. Restex s corporate tax rate s 40%, and ts market captalzaton s $220 mllon. a. If Restex s free cash flow s expected to be $ mllon n one year, what constant expected future growth rate s consstent wth the frm s current market value? b. Estmate the value of Restex s nterest tax sheld = 12% + 7% 0.40 = 8.42% L FF V = E+ D = = 407 = = WA g g g = = 5.96% 407 a. WA ( ) b pretax WA = 12% + 7% = 9.70% FF = = = $267 mllon pretax WA g PV Interest Tax Sheld = = $140 mllon U V ( )
5 Berk/DeMarzo orporate Fnance, Second Edton Acme Storage has a market captalzaton of $0 mllon and debt outstandng of $40 mllon. Acme plans to mantan ths same debtequty rato n the future. The frm pays an nterest rate of 7.5% on ts debt and has a corporate tax rate of 35%. a. If Acme s free cash flow s expected to be $7 mllon next year and s expected to grow at a rate of 3% per year, what s Acme s WA? b. What s the value of Acme s nterest tax sheld? a. L FF 7 V = E+ D = 140 = =. Therefore WA = 8%. WA g WA 3% 40 WA = WA + D rd 8% 7.5% % E+ D τ = = b. Pretax ( )( ) U FF 7 V = = = $122 mllon pretax WA g L U PV Interest Tax Sheld = V V = = $18 mllon ( ) Mlton Industres expects free cash flow of $5 mllon each year. Mlton s corporate tax rate s 35%, and ts unlevered cost of captal s 15%. The frm also has outstandng debt of $19.05 mllon, and t expects to mantan ths level of debt permanently. a. What s the value of Mlton Industres wthout leverage? b. What s the value of Mlton Industres wth leverage? a. U 5 V = = $33.33 mllon 0.15 L U b. V = V + τ D = = $40 mllon Suppose Mcrosoft has 8.75 bllon shares outstandng and pays a margnal corporate tax rate of 35%. If Mcrosoft announces that t wll payout $50 bllon n cash to nvestors through a combnaton of a specal dvdend and a share repurchase, and f nvestors had prevously assumed Mcrosoft would retan ths excess cash permanently, by how much wll Mcrosoft s share prce change upon the announcement? Reducng cash s equvalent to ncreasng leverage by $50 bllon. PV of tax savngs = 35% 50 = $17.5 bllon, or 17.5/ 8.75 = $2.00 per share prce ncrease Kurz Manufacturng s currently an allequty frm wth 20 mllon shares outstandng and a stock prce of $7.50 per share. Although nvestors currently expect Kurz to reman an allequty frm, Kurz plans to announce that t wll borrow $50 mllon and use the funds to repurchase shares. Kurz wll pay nterest only on ths debt, and t has no further plans to ncrease or decrease the amount of debt. Kurz s subject to a 40% corporate tax rate. a. What s the market value of Kurz s exstng assets before the announcement? b. What s the market value of Kurz s assets (ncludng any tax shelds) just after the debt s ssued, but before the shares are repurchased? c. What s Kurz s share prce just before the share repurchase? How many shares wll Kurz repurchase? d. What are Kurz s market value balance sheet and share prce after the share repurchase? a. Assets = Equty = $ = $150 mllon b. Assets = 150 (exstng) + 50 (cash) + 40% 50 (tax sheld) = $220 mllon
6 198 Berk/DeMarzo orporate Fnance, Second Edton c. E = Assets Debt = = $170 mllon. Share prce $170 mllon = = $ Kurz wll repurchase = mllon shares d. Assets = 150 (exstng) + 40% 50 (tax sheld) = $170 mllon Debt = $50 mllon E = A D = = $120 mllon $120 Share prce = = $8.50 / share Rally, Inc., s an allequty frm wth assets worth $25 bllon and bllon shares outstandng. Rally plans to borrow $ bllon and use these funds to repurchase shares. The frm s corporate tax rate s 35%, and Rally plans to keep ts outstandng debt equal to $ bllon permanently. a. Wthout the ncrease n leverage, what would Rally s share prce be? b. Suppose Rally offers $2.75 per share to repurchase ts shares. Would shareholders sell for ths prce? c. Suppose Rally offers $3.00 per share, and shareholders tender ther shares at ths prce. What wll Rally s share prce be after the repurchase? d. What s the lowest prce Rally can offer and have shareholders tender ther shares? What wll ts stock prce be after the share repurchase n that case? 25 a. Share prce = = $2.50 per share b. Just before the share repurchase: Assets = 25( exstng) + ( cash) + 35% ( tax sheld ) = $38.5 bllon 28.5 E = 38.5 = 28.5Þshare prce = = $2.85/ share. Therefore, shareholders wll not sell for $2.75 per share. c. Assets = 25 (exstng) + 35% (tax sheld) = $28.5 bllon E = 28.5 = 18.5 bllon 18.5 Shares = = bllon. Share prce = = $2.775 share d. From (b), far value of the shares pror to repurchase s $2.85. At ths prce, Rally wll have = 6.49 mllon shares outstandng, whch wll be worth 18.5 = $2.85 after the repurchase. Therefore, shares wll be wllng to sell at ths prce Suppose the corporate tax rate s 40%, and nvestors pay a tax rate of 15% on ncome from dvdends or captal gans and a tax rate of 33.3% on nterest ncome. Your frm decdes to add debt so t wll pay an addtonal $15 mllon n nterest each year. It wll pay ths nterest expense by cuttng ts dvdend. a. How much wll debt holders receve after payng taxes on the nterest they earn? b. By how much wll the frm need to cut ts dvdend each year to pay ths nterest expense?
7 Berk/DeMarzo orporate Fnance, Second Edton 199 c. By how much wll ths cut n the dvdend reduce equty holders annual aftertax ncome? d. How much less wll the government receve n total tax revenues each year? e. What s the effectve tax advantage of debt τ*? a. $15 (1.333) = $ mllon each year b. Gven a corporate tax rate of 40%, an nterest expense of $15 mllon per year reduces net ncome by 15(1.4) = $9 mllon after corporate taxes. c. $9 mllon dvdend cut $9 (1.15) = $7.65 mllon per year. d. Interest taxes = = $5 mllon Less corporate taxes = = $6 mllon Less dvdend taxes =.15 9 = $1.35 mllon e. Govt tax revenues change by = $2.35 mllon (Note ths equals (a) (c)). ( 0.40)( 0.15) τ* = = 23.5% Apple orporaton had no debt on ts balance sheet n 2008, but pad $2 bllon n taxes. Suppose Apple were to ssue suffcent debt to reduce ts taxes by $1 bllon per year permanently. Assume Apple s margnal corporate tax rate s 35% and ts borrowng cost s 7.5%. a. If Apple s nvestors do not pay personal taxes (because they hold ther Apple stock n taxfree retrement accounts), how much value would be created (what s the value of the tax sheld)? b. How does your answer change f nstead you assume that Apple s nvestors pay a 15% tax rate on ncome from equty and a 35% tax rate on nterest ncome? a. $1 bllon / 7.5% = $13.33 bllon. b. To reduce taxes by $1 bllon, Apple wll need to make nterest payments of 1/.35 = $2.857 bllon, or ssue 2.857/.075 = $38.1 bllon n debt. T = 1 (1 tc)(1 te)/(1 t) = 1 (.65)(.85)/.65 = 15% T D = 15% $38.1 = $5.71 bllon Markum Enterprses s consderng permanently addng $0 mllon of debt to ts captal structure. Markum s corporate tax rate s 35%. a. Absent personal taxes, what s the value of the nterest tax sheld from the new debt? b. If nvestors pay a tax rate of 40% on nterest ncome, and a tax rate of 20% on ncome from dvdends and captal gans, what s the value of the nterest tax sheld from the new debt? a. PV = τ D = 35% 0 = $35 mllon. b. ( 0.35)( 0.20) τ* = = 13.33% 0.40 PV = τ D = 13.33% 0 = $13.33 mllon Garnet orporaton s consderng ssung rskfree debt or rskfree preferred stock. The tax rate on nterest ncome s 35%, and the tax rate on dvdends or captal gans from preferred
8 200 Berk/DeMarzo orporate Fnance, Second Edton stock s 15%. However, the dvdends on preferred stock are not deductble for corporate tax purposes, and the corporate tax rate s 40%. a. If the rskfree nterest rate for debt s 6%, what s cost of captal for rskfree preferred stock? b. What s the aftertax debt cost of captal for the frm? Whch securty s cheaper for the frm? c. Show that the aftertax debt cost of captal s equal to the preferred stock cost of captal multpled by (1 τ*). a. Investors receve 6% (1.35) = 3.9% aftertax from rskfree debt. They must earn the same aftertax return from rskfree preferred stock. Therefore, the cost of captal for preferred stock s 3.9% 0.15% = 4.59%. b. Aftertax debt cost of captal = 6% (1.40) = 3.60% s cheaper than the 4.59% cost of captal for preferred stock. ( 0.40)( 0.15) c. τ* = = 21.54% % (1.2154) = 3.60% Suppose the tax rate on nterest ncome s 35%, and the average tax rate on captal gans and dvdend ncome s %. How hgh must the margnal corporate tax rate be for debt to offer a tax advantage? ( )( e) τ* = > 0 f and only f τ < or equvalently: 1 τ e 0.65 τ > = = 27.8% Thus, there s a tax advantage of debt as long as the margnal corporate tax rate s above 27.8% Wth ts current leverage, Imp orporaton wll have net ncome next year of $4.5 mllon. If Imp s corporate tax rate s 35% and t pays 8% nterest on ts debt, how much addtonal debt can Imp ssue ths year and stll receve the beneft of the nterest tax sheld next year? 4.5 Net ncome of $4.5 mllon 0.35 = $6.923 mllon n taxable ncome. Therefore, Arundel can ncrease ts nterest expenses by $6.923 mllon, whch corresponds to debt of: $ = mllon olt Systems wll have EBIT ths comng year of $15 mllon. It wll also spend $6 mllon on total captal expendtures and ncreases n net workng captal, and have $3 mllon n deprecaton expenses. olt s currently an allequty frm wth a corporate tax rate of 35% and a cost of captal of %. a. If olt s expected to grow by 8.5% per year, what s the market value of ts equty today? b. If the nterest rate on ts debt s 8%, how much can olt borrow now and stll have nonnegatve net ncome ths comng year? c. Is there a tax ncentve for olt to choose a debttovalue rato that exceeds 50%? Explan. e
9 Berk/DeMarzo orporate Fnance, Second Edton 201 a. FF EBIT ( τ ) Dep apex NW ( ) = + Δ = = E = = $450 mllon % 8.5% b. 15 Interest expense of $15 mllon debt of $ = mllon. c. No. The most they should borrow s mllon; there s no nterest tax sheld from borrowng more PMF, Inc., s equally lkely to have EBIT ths comng year of $ mllon, $15 mllon, or $20 mllon. Its corporate tax rate s 35%, and nvestors pay a 15% tax rate on ncome from equty and a 35% tax rate on nterest ncome. a. What s the effectve tax advantage of debt f PMF has nterest expenses of $8 mllon ths comng year? b. What s the effectve tax advantage of debt for nterest expenses n excess of $20 mllon? (Ignore carryforwards.) c. What s the expected effectve tax advantage of debt for nterest expenses between $ mllon and $15 mllon? (Ignore carryforwards.) d. What level of nterest expense provdes PMF wth the greatest tax beneft? ( )( e) ( 0.35)( 0.15) a. τ* = = = 15% 0.35 b. For nterest expenses over $20 mllon, net ncome s negatve so τ = 0. ( )( e) ( 0)( 0.15) Therefore, τ* = = = 31% 0.35 c. For nterest expenses between $ mllon and $15 mllon, there s a 2 3 chance that net ncome wll be postve. Therefore, the expected corporate tax savngs s 2 35% 23.3% 3 =. Thus, ( )( ) ( 0.23)( 0.15) e τ* = = = 0.3% d. There s a tax advantage up to an nterest expense of $ mllon.
Chapter 15: Debt and Taxes
Chapter 15: Debt and Taxes1 Chapter 15: Debt and Taxes I. Basc Ideas 1. Corporate Taxes => nterest expense s tax deductble => as debt ncreases, corporate taxes fall => ncentve to fund the frm wth debt
More informationSolution: Let i = 10% and d = 5%. By definition, the respective forces of interest on funds A and B are. i 1 + it. S A (t) = d (1 dt) 2 1. = d 1 dt.
Chapter 9 Revew problems 9.1 Interest rate measurement Example 9.1. Fund A accumulates at a smple nterest rate of 10%. Fund B accumulates at a smple dscount rate of 5%. Fnd the pont n tme at whch the forces
More information10. (# 45, May 2001). At time t = 0, 1 is deposited into each of Fund X and Fund Y. Fund X accumulates at a force of interest
1 Exam FM questons 1. (# 12, May 2001). Bruce and Robbe each open up new bank accounts at tme 0. Bruce deposts 100 nto hs bank account, and Robbe deposts 50 nto hs. Each account earns an annual e ectve
More information0.02t if 0 t 3 δ t = 0.045 if 3 < t
1 Exam FM questons 1. (# 12, May 2001). Bruce and Robbe each open up new bank accounts at tme 0. Bruce deposts 100 nto hs bank account, and Robbe deposts 50 nto hs. Each account earns an annual effectve
More informationSection 2.3 Present Value of an Annuity; Amortization
Secton 2.3 Present Value of an Annuty; Amortzaton Prncpal Intal Value PV s the present value or present sum of the payments. PMT s the perodc payments. Gven r = 6% semannually, n order to wthdraw $1,000.00
More informationSimple Interest Loans (Section 5.1) :
Chapter 5 Fnance The frst part of ths revew wll explan the dfferent nterest and nvestment equatons you learned n secton 5.1 through 5.4 of your textbook and go through several examples. The second part
More informationAn Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationSection 5.4 Annuities, Present Value, and Amortization
Secton 5.4 Annutes, Present Value, and Amortzaton Present Value In Secton 5.2, we saw that the present value of A dollars at nterest rate per perod for n perods s the amount that must be deposted today
More informationFINANCIAL MATHEMATICS
3 LESSON FINANCIAL MATHEMATICS Annutes What s an annuty? The term annuty s used n fnancal mathematcs to refer to any termnatng sequence of regular fxed payments over a specfed perod of tme. Loans are usually
More information7.5. Present Value of an Annuity. Investigate
7.5 Present Value of an Annuty Owen and Anna are approachng retrement and are puttng ther fnances n order. They have worked hard and nvested ther earnngs so that they now have a large amount of money on
More informationAnswer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy
4.02 Quz Solutons Fall 2004 MultpleChoce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multplechoce questons. For each queston, only one of the answers s correct.
More informationTime Value of Money. Types of Interest. Compounding and Discounting Single Sums. Page 1. Ch. 6  The Time Value of Money. The Time Value of Money
Ch. 6  The Tme Value of Money Tme Value of Money The Interest Rate Smple Interest Compound Interest Amortzng a Loan FIN21 Ahmed Y, Dasht TIME VALUE OF MONEY OR DISCOUNTED CASH FLOW ANALYSIS Very Important
More informationU + PV(Interest Tax Shield)
CHAPTER 15 Debt and Taxes Chapter Synopsis 15.1 The Interest Tax Deduction A CCorporation pays taxes on proits ater interest payments are deducted, but it pays dividends rom atertax net income. Thus,
More information3. Present value of Annuity Problems
Mathematcs of Fnance The formulae 1. A = P(1 +.n) smple nterest 2. A = P(1 + ) n compound nterest formula 3. A = P(1.n) deprecaton straght lne 4. A = P(1 ) n compound decrease dmshng balance 5. P = 
More informationUsing Series to Analyze Financial Situations: Present Value
2.8 Usng Seres to Analyze Fnancal Stuatons: Present Value In the prevous secton, you learned how to calculate the amount, or future value, of an ordnary smple annuty. The amount s the sum of the accumulated
More informationFinite Math Chapter 10: Study Guide and Solution to Problems
Fnte Math Chapter 10: Study Gude and Soluton to Problems Basc Formulas and Concepts 10.1 Interest Basc Concepts Interest A fee a bank pays you for money you depost nto a savngs account. Prncpal P The amount
More informationConstruction Rules for Morningstar Canada Target Dividend Index SM
Constructon Rules for Mornngstar Canada Target Dvdend Index SM Mornngstar Methodology Paper October 2014 Verson 1.2 2014 Mornngstar, Inc. All rghts reserved. The nformaton n ths document s the property
More informationSection 5.3 Annuities, Future Value, and Sinking Funds
Secton 5.3 Annutes, Future Value, and Snkng Funds Ordnary Annutes A sequence of equal payments made at equal perods of tme s called an annuty. The tme between payments s the payment perod, and the tme
More informationFINANCIAL MATHEMATICS. A Practical Guide for Actuaries. and other Business Professionals
FINANCIAL MATHEMATICS A Practcal Gude for Actuares and other Busness Professonals Second Edton CHRIS RUCKMAN, FSA, MAAA JOE FRANCIS, FSA, MAAA, CFA Study Notes Prepared by Kevn Shand, FSA, FCIA Assstant
More informationProblem Set 3. a) We are asked how people will react, if the interest rate i on bonds is negative.
Queston roblem Set 3 a) We are asked how people wll react, f the nterest rate on bonds s negatve. When
More informationGESTÃO FINANCEIRA II PROBLEM SET 5 SOLUTIONS (FROM BERK AND DEMARZO S CORPORATE FINANCE ) LICENCIATURA UNDERGRADUATE COURSE
GESTÃO FINANCEIRA II PROBLEM SET 5 SOLUTIONS (FROM BERK AND DEMARZO S CORPORATE FINANCE ) LICENCIATURA UNDERGRADUATE COURSE 1 ST SEMESTER 20102011 Chapter 18 Capital Budgeting and Valuation with Leverage
More informationA) 3.1 B) 3.3 C) 3.5 D) 3.7 E) 3.9 Solution.
ACTS 408 Instructor: Natala A. Humphreys SOLUTION TO HOMEWOR 4 Secton 7: Annutes whose payments follow a geometrc progresson. Secton 8: Annutes whose payments follow an arthmetc progresson. Problem Suppose
More informationNumber of Levels Cumulative Annual operating Income per year construction costs costs ($) ($) ($) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000
Problem Set 5 Solutons 1 MIT s consderng buldng a new car park near Kendall Square. o unversty funds are avalable (overhead rates are under pressure and the new faclty would have to pay for tself from
More information10.2 Future Value and Present Value of an Ordinary Simple Annuity
348 Chapter 10 Annutes 10.2 Future Value and Present Value of an Ordnary Smple Annuty In compound nterest, 'n' s the number of compoundng perods durng the term. In an ordnary smple annuty, payments are
More informationChapter 11 Practice Problems Answers
Chapter 11 Practce Problems Answers 1. Would you be more wllng to lend to a frend f she put all of her lfe savngs nto her busness than you would f she had not done so? Why? Ths problem s ntended to make
More informationLecture 3: Annuity. Study annuities whose payments form a geometric progression or a arithmetic progression.
Lecture 3: Annuty Goals: Learn contnuous annuty and perpetuty. Study annutes whose payments form a geometrc progresson or a arthmetc progresson. Dscuss yeld rates. Introduce Amortzaton Suggested Textbook
More informationMathematics of Finance
Mathematcs of Fnance 5 C H A P T E R CHAPTER OUTLINE 5.1 Smple Interest and Dscount 5.2 Compound Interest 5.3 Annutes, Future Value, and Snkng Funds 5.4 Annutes, Present Value, and Amortzaton CASE STUDY
More informationCHAPTER 18. Capital Budgeting and Valuation with Leverage. Chapter Synopsis
CHAPTER 18 Capital Budgeting and Valuation with everage Chapter Synopsis 18.1 Overview of Key Concepts There are three discounted cash flow valuation methods: the weighted average cost of capital (WACC)
More informationMathematics of Finance
CHAPTER 5 Mathematcs of Fnance 5.1 Smple and Compound Interest 5.2 Future Value of an Annuty 5.3 Present Value of an Annuty; Amortzaton Revew Exercses Extended Applcaton: Tme, Money, and Polynomals Buyng
More informationEXAMPLE PROBLEMS SOLVED USING THE SHARP EL733A CALCULATOR
EXAMPLE PROBLEMS SOLVED USING THE SHARP EL733A CALCULATOR 8S CHAPTER 8 EXAMPLES EXAMPLE 8.4A THE INVESTMENT NEEDED TO REACH A PARTICULAR FUTURE VALUE What amount must you nvest now at 4% compoune monthly
More informationChapter 14 Capital Structure in a Perfect Market
Chapter 14 Capital Structure in a Perfect Market 141. Consider a project with free cash flows in one year of $130,000 or $180,000, with each outcome being equally likely. The initial investment required
More informationIntrayear Cash Flow Patterns: A Simple Solution for an Unnecessary Appraisal Error
Intrayear Cash Flow Patterns: A Smple Soluton for an Unnecessary Apprasal Error By C. Donald Wggns (Professor of Accountng and Fnance, the Unversty of North Florda), B. Perry Woodsde (Assocate Professor
More informationRob Guthrie, Business Initiatives Specialist Office of Renewable Energy & Environmental Exports
Fnancng Solar Energy Exports Rob Guthre, Busness Intatves Specalst Offce of Renewable Energy & Envronmental Exports ExportImport Bank of the U.S. Independent, selffundng fundng agency of the U.S. government
More informationMorningstar AfterTax Return Methodology
Mornngstar AfterTax Return Methodology Mornngstar Research Report March 1, 2013 2013 Mornngstar, Inc. All rghts reserved. The nformaton n ths document s the property of Mornngstar, Inc. Reproducton or
More informationDUKE UNIVERSITY Fuqua School of Business. FINANCE 351  CORPORATE FINANCE Problem Set #4 Prof. Simon Gervais Fall 2011 Term 2.
DUK UNIRSITY Fuqua School of Business FINANC 351  CORPORAT FINANC Problem Set #4 Prof. Simon Gervais Fall 2011 Term 2 Questions 1. Suppose the corporate tax rate is 40%. Consider a firm that earns $1,000
More informationSTAMP DUTY ON SHARES AND ITS EFFECT ON SHARE PRICES
STAMP UTY ON SHARES AN ITS EFFECT ON SHARE PRICES Steve Bond Mke Hawkns Alexander Klemm THE INSTITUTE FOR FISCAL STUIES WP04/11 STAMP UTY ON SHARES AN ITS EFFECT ON SHARE PRICES Steve Bond (IFS and Unversty
More informationLIFETIME INCOME OPTIONS
LIFETIME INCOME OPTIONS May 2011 by: Marca S. Wagner, Esq. The Wagner Law Group A Professonal Corporaton 99 Summer Street, 13 th Floor Boston, MA 02110 Tel: (617) 3575200 Fax: (617) 3575250 www.ersalawyers.com
More informationIn our example i = r/12 =.0825/12 At the end of the first month after your payment is received your amount owed is. P (1 + i) A
Amortzed loans: Suppose you borrow P dollars, e.g., P = 100, 000 for a house wth a 30 year mortgage wth an nterest rate of 8.25% (compounded monthly). In ths type of loan you make equal payments of A dollars
More informationUncrystallised funds pension lump sum payment instruction
For customers Uncrystallsed funds penson lump sum payment nstructon Don t complete ths form f your wrapper s derved from a penson credt receved followng a dvorce where your ex spouse or cvl partner had
More information1. Math 210 Finite Mathematics
1. ath 210 Fnte athematcs Chapter 5.2 and 5.3 Annutes ortgages Amortzaton Professor Rchard Blecksmth Dept. of athematcal Scences Northern Illnos Unversty ath 210 Webste: http://math.nu.edu/courses/math210
More informationreduce competition increase market power cost savings economies of scale and scope cost savings Oliver Williamson: the efficiency defense
Mergers Why merge? reduce competton ncrease market power cost savngs economes of scale and scope Why allow mergers? cost savngs Olver Wllamson: the effcency defense Merger wthout cost savngs Before merger:
More informationCHAPTER 15 Capital Structure: Basic Concepts
Multiple Choice Questions: CHAPTER 15 Capital Structure: Basic Concepts I. DEFINITIONS HOMEMADE LEVERAGE a 1. The use of personal borrowing to change the overall amount of financial leverage to which an
More informationMathematics of Finance
5 Mathematcs of Fnance 5.1 Smple and Compound Interest 5.2 Future Value of an Annuty 5.3 Present Value of an Annuty;Amortzaton Chapter 5 Revew Extended Applcaton:Tme, Money, and Polynomals Buyng a car
More informationStress test for measuring insurance risks in nonlife insurance
PROMEMORIA Datum June 01 Fnansnspektonen Författare Bengt von Bahr, Younes Elonq and Erk Elvers Stress test for measurng nsurance rsks n nonlfe nsurance Summary Ths memo descrbes stress testng of nsurance
More informationThursday, December 10, 2009 Noon  1:50 pm Faraday 143
1. ath 210 Fnte athematcs Chapter 5.2 and 4.3 Annutes ortgages Amortzaton Professor Rchard Blecksmth Dept. of athematcal Scences Northern Illnos Unversty ath 210 Webste: http://math.nu.edu/courses/math210
More informationFinancial Mathemetics
Fnancal Mathemetcs 15 Mathematcs Grade 12 Teacher Gude Fnancal Maths Seres Overvew In ths seres we am to show how Mathematcs can be used to support personal fnancal decsons. In ths seres we jon Tebogo,
More informationInstitute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic
Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange
More informationHollinger Canadian Publishing Holdings Co. ( HCPH ) proceeding under the Companies Creditors Arrangement Act ( CCAA )
February 17, 2011 Andrew J. Hatnay ahatnay@kmlaw.ca Dear Sr/Madam: Re: Re: Hollnger Canadan Publshng Holdngs Co. ( HCPH ) proceedng under the Companes Credtors Arrangement Act ( CCAA ) Update on CCAA Proceedngs
More informationStaff Paper. Farm Savings Accounts: Examining Income Variability, Eligibility, and Benefits. Brent Gloy, Eddy LaDue, and Charles Cuykendall
SP 200502 August 2005 Staff Paper Department of Appled Economcs and Management Cornell Unversty, Ithaca, New York 148537801 USA Farm Savngs Accounts: Examnng Income Varablty, Elgblty, and Benefts Brent
More informationOutline. Investment Opportunity Set with Many Assets. Portfolio Selection with Multiple Risky Securities. Professor Lasse H.
Portfolo Selecton wth Multple Rsky Securtes. Professor Lasse H. Pedersen Prof. Lasse H. Pedersen Outlne Investment opportunty set wth many rsky assets wth many rsky assets and a rskfree securty Optmal
More informationFinancial Markets and Valuation  Tutorial 6: SOLUTIONS. Capital Structure and Cost of Funds
Financial Markets and Valuation  Tutorial 6: SOLUTIONS Capital Structure and Cost of Funds (*) denotes those problems to be covered in detail during the tutorial session (*) Problem 1. (Ross, Westerfield
More informationNew evidence of the impact of dividend taxation and on the identity of the marginal investor
New evdence of the mpact of dvdend taxaton and on the dentty of the margnal nvestor LEONIE BELL AND TIM JENKINSON * * Economcs Department, Oxford Unversty and Saïd Busness School, Oxford Unversty and CEPR
More informationSection 2.2 Future Value of an Annuity
Secton 2.2 Future Value of an Annuty Annuty s any sequence of equal perodc payments. Depost s equal payment each nterval There are two basc types of annutes. An annuty due requres that the frst payment
More informationDo stock prices underreact to SEO announcements? Evidence from SEO Valuation
Do stock prces underreact to SEO announcements? Evdence from SEO Valuaton Amyatosh K. Purnanandam Bhaskaran Swamnathan * Frst Draft: December 2005 Comments Welcome * Purnanandam s an Assstant Professor
More informationReporting Instructions for Schedules A through S
FFIEC 0 Reportng Instructons for Schedules A through S FFIEC 0 FFIEC 0 CONTENTS INSTRUCTIONS FOR PREPARATION OF FFIEC 0 RskBased Captal Reportng for Insttutons Subject to the Advanced Captal Adequacy
More informationHealth Insurance and Household Savings
Health Insurance and Household Savngs Mnchung Hsu Job Market Paper Last Updated: November, 2006 Abstract Recent emprcal studes have documented a puzzlng pattern of household savngs n the U.S.: households
More informationMarginal Returns to Education For Teachers
The Onlne Journal of New Horzons n Educaton Volume 4, Issue 3 MargnalReturnstoEducatonForTeachers RamleeIsmal,MarnahAwang ABSTRACT FacultyofManagementand Economcs UnverstPenddkanSultan Idrs ramlee@fpe.ups.edu.my
More informationINTRODUCTION TO MERGERS AND ACQUISITIONS: FIRM DIVERSIFICATION
XV. INTODUCTION TO MEGES AND ACQUISITIONS: FIM DIVESIFICATION In the ntroducton to Secton VII, t was noted that frs can acqure assets by ether undertakng nternallygenerated new projects or by acqurng
More informationFinance 2 for IBA (30J201) F.Feriozzi Regular exam December 15 th, 2010. Part One: MultipleChoice Questions (45 points)
Finance 2 for IBA (30J201) F.Feriozzi Regular exam December 15 th, 2010 Question 1 Part One: Multiplehoice Questions (45 points) Which of the following statements regarding the capital structure decision
More informationChapter 16 Financial Distress, Managerial Incentives, and Information
Chapter 16 Financial Distress, Managerial Incentives, and Information 161. Gladstone Corporation is about to launch a new product. Depending on the success of the new product, Gladstone may have one of
More informationReporting Forms ARF 113.0A, ARF 113.0B, ARF 113.0C and ARF 113.0D FIRB Corporate (including SME Corporate), Sovereign and Bank Instruction Guide
Reportng Forms ARF 113.0A, ARF 113.0B, ARF 113.0C and ARF 113.0D FIRB Corporate (ncludng SME Corporate), Soveregn and Bank Instructon Gude Ths nstructon gude s desgned to assst n the completon of the FIRB
More information1 Pricing options using the Black Scholes formula
Lecture 9 Pricing options using the Black Scholes formula Exercise. Consider month options with exercise prices of K = 45. The variance of the underlying security is σ 2 = 0.20. The risk free interest
More informationDepreciation of Business R&D Capital
Deprecaton of Busness R&D Captal U.S. Bureau of Economc Analyss Abstract R&D deprecaton rates are crtcal to calculatng the rates of return to R&D nvestments and captal servce costs, whch are mportant for
More informationWeek 6 Market Failure due to Externalities
Week 6 Market Falure due to Externaltes 1. Externaltes n externalty exsts when the acton of one agent unavodably affects the welfare of another agent. The affected agent may be a consumer, gvng rse to
More informationTexas Instruments 30Xa Calculator
Teas Instruments 30Xa Calculator Keystrokes for the TI30Xa are shown for a few topcs n whch keystrokes are unque. Start by readng the Quk Start secton. Then, before begnnng a specfc unt of the tet, check
More informationSmall pots lump sum payment instruction
For customers Small pots lump sum payment nstructon Please read these notes before completng ths nstructon About ths nstructon Use ths nstructon f you re an ndvdual wth Aegon Retrement Choces Self Invested
More informationANALYSIS OF FINANCIAL FLOWS
ANALYSIS OF FINANCIAL FLOWS AND INVESTMENTS II 4 Annutes Only rarely wll one encounter an nvestment or loan where the underlyng fnancal arrangement s as smple as the lump sum, sngle cash flow problems
More informationMoving Beyond Open Markets for Water Quality Trading: The Gains from Structured Bilateral Trades
Movng Beyond Open Markets for Water Qualty Tradng: The Gans from Structured Blateral Trades Tanl Zhao Yukako Sado Rchard N. Bosvert Gregory L. Poe Cornell Unversty EAERE Preconference on Water Economcs
More informationDO LOSS FIRMS MANAGE EARNINGS AROUND SEASONED EQUITY OFFERINGS?
DO LOSS FIRMS MANAGE EARNINGS AROUND SEASONED EQUITY OFFERINGS? Fernando Comran, Unversty of San Francsco, School of Management, 2130 Fulton Street, CA 94117, Unted States, fcomran@usfca.edu Tatana Fedyk,
More informationCost of Capital and Project Valuation
Cost of Capital and Project Valuation 1 Background Firm organization There are four types: sole proprietorships partnerships limited liability companies corporations Each organizational form has different
More informationAmeriprise Financial Services, Inc. or RiverSource Life Insurance Company Account Registration
CED0105200808 Amerprse Fnancal Servces, Inc. 70400 Amerprse Fnancal Center Mnneapols, MN 55474 Incomng Account Transfer/Exchange/ Drect Rollover (Qualfed Plans Only) for Amerprse certfcates, Columba mutual
More informationMM1  The value of the firm is independent of its capital structure (the proportion of debt and equity used to finance the firm s operations).
Teaching Note Miller Modigliani Consider an economy for which the Efficient Market Hypothesis holds and in which all financial assets are possibly traded (abusing words we call this The Complete Markets
More informationCHAPTER 17. Payout Policy. Chapter Synopsis
CHAPTER 17 Payout Policy Chapter Synopsis 17.1 Distributions to Shareholders A corporation s payout policy determines if and when it will distribute cash to its shareholders by issuing a dividend or undertaking
More informationISLM Model 1 C' dy = di
 odel Solow Assumptons  demand rrelevant n long run; assumes economy s operatng at potental GDP; concerned wth growth  Assumptons  supply s rrelevant n short run; assumes economy s operatng below potental
More informationA Critical Note on MCEV Calculations Used in the Life Insurance Industry
A Crtcal Note on MCEV Calculatons Used n the Lfe Insurance Industry Faban Suarez 1 and Steven Vanduffel 2 Abstract. Snce the begnnng of the development of the socalled embedded value methodology, actuares
More informationMost investors focus on the management
LongShort Portfolo Management: An Integrated Approach The real benefts of longshort are released only by an ntegrated portfolo optmzaton. Bruce I. Jacobs, Kenneth. Levy, and Davd Starer BRUCE I. JACOBS
More informationUse the table for the questions 18 and 19 below.
Use the table for the questions 18 and 19 below. The following table summarizes prices of various defaultfree zerocoupon bonds (expressed as a percentage of face value): Maturity (years) 1 3 4 5 Price
More informationbenefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).
REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or
More informationFinance 2 for IBA (30J201) F.Feriozzi Resit exam June 14 th, 2011. Part One: MultipleChoice Questions (45 points)
Question 1 Finance 2 for IBA (30J201) F.Feriozzi Resit exam June 14 th, 2011 Part One: MultipleChoice Questions (45 points) Assume that financial markets are perfect and that the market value of a levered
More informationADVA FINAN QUAN ADVANCED FINANCE AND QUANTITATIVE INTERVIEWS VAULT GUIDE TO. Customized for: Jason (jason.barquero@cgu.edu) 2002 Vault Inc.
ADVA FINAN QUAN 00 Vault Inc. VAULT GUIDE TO ADVANCED FINANCE AND QUANTITATIVE INTERVIEWS Copyrght 00 by Vault Inc. All rghts reserved. All nformaton n ths book s subject to change wthout notce. Vault
More informationEMBA in Management & Finance. Corporate Finance. Eric Jondeau
EMBA in Management & Finance Corporate Finance EMBA in Management & Finance Lecture 5: Capital Budgeting For the Levered Firm Prospectus Recall that there are three questions in corporate finance. The
More informationAbstract # 0150399 Working Capital Exposure: A Methodology to Control Economic Performance in Production Environment Projects
Abstract # 0150399 Workng Captal Exposure: A Methodology to Control Economc Performance n Producton Envronment Projects Dego F. Manotas. School of Industral Engneerng and Statstcs, Unversdad del Valle.
More information17 Capital tax competition
17 Captal tax competton 17.1 Introducton Governments would lke to tax a varety of transactons that ncreasngly appear to be moble across jursdctonal boundares. Ths creates one obvous problem: tax base flght.
More informationFirst name Middle name Last name PAN. Individual HUF Road/Street/Post Office Area/locality Date of Birth/Formation (DD/MM/YYYY)
TOTAL NCOME FLNG STATUS PERSONAL NFORMATON FORM TR2 NDAN NCOME TAX RETURN [For ndvduals and HUFs not havng ncome from Busness or Professon] (Please see Rule 12 of the ncometax Rules,1962) (Also see attached
More informationGender differences in revealed risk taking: evidence from mutual fund investors
Economcs Letters 76 (2002) 151 158 www.elsever.com/ locate/ econbase Gender dfferences n revealed rsk takng: evdence from mutual fund nvestors a b c, * Peggy D. Dwyer, James H. Glkeson, John A. Lst a Unversty
More informationMultiplePeriod Attribution: Residuals and Compounding
MultplePerod Attrbuton: Resduals and Compoundng Our revewer gave these authors full marks for dealng wth an ssue that performance measurers and vendors often regard as propretary nformaton. In 1994, Dens
More informationR RiskBased Global Developed Markets Equity Index. Methodology
R RskBased Global Developed Markets Equty Index Methodology R RskBased Global Developed Markets Equty Index Fnal Documentaton Dsclamer Rsk Based Investment Solutons Ltd ("RBIS") 2014. RBIS s the Index
More informationTHE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek
HE DISRIBUION OF LOAN PORFOLIO VALUE * Oldrch Alfons Vascek he amount of captal necessary to support a portfolo of debt securtes depends on the probablty dstrbuton of the portfolo loss. Consder a portfolo
More informationTime Value of Money Module
Tme Value of Money Module O BJECTIVES After readng ths Module, you wll be able to: Understand smple nterest and compound nterest. 2 Compute and use the future value of a sngle sum. 3 Compute and use the
More informationLECTURE 09. Valuation Berk, De Marzo Chapter 18
1 LECTURE 09 Valuation Berk, De Marzo Chapter 18 2 Overview of Key Concepts Assumptions in this chapter The project has average risk. The firm s debtequity ratio is constant. Corporate taxes are the only
More informationTexas Instruments 30X IIS Calculator
Texas Instruments 30X IIS Calculator Keystrokes for the TI30X IIS are shown for a few topcs n whch keystrokes are unque. Start by readng the Quk Start secton. Then, before begnnng a specfc unt of the
More informationA Master Time Value of Money Formula. Floyd Vest
A Master Tme Value of Money Formula Floyd Vest For Fnancal Functons on a calculator or computer, Master Tme Value of Money (TVM) Formulas are usually used for the Compound Interest Formula and for Annutes.
More informationCHAPTER 20. Hybrid Financing: Preferred Stock, Warrants, and Convertibles
CHAPTER 20 Hybrid Financing: Preferred Stock, Warrants, and Convertibles 1 Topics in Chapter Types of hybrid securities Preferred stock Warrants Convertibles Features and risk Cost of capital to issuers
More informationThe CoxRossRubinstein Option Pricing Model
Fnance 400 A. Penat  G. Pennacc Te CoxRossRubnsten Opton Prcng Model Te prevous notes sowed tat te absence o arbtrage restrcts te prce o an opton n terms o ts underlyng asset. However, te noarbtrage
More informationInterest Rate Futures
Interest Rate Futures Chapter 6 6.1 Day Count Conventons n the U.S. (Page 129) Treasury Bonds: Corporate Bonds: Money Market Instruments: Actual/Actual (n perod) 30/360 Actual/360 The day count conventon
More informationUncrystallised funds pension lump sum
For customers Uncrystallsed funds penson lump sum Payment nstructon What does ths form do? Ths form nstructs us to pay the full penson fund, under your nonoccupatonal penson scheme plan wth us, to you
More informationLecture 3: Force of Interest, Real Interest Rate, Annuity
Lecture 3: Force of Interest, Real Interest Rate, Annuty Goals: Study contnuous compoundng and force of nterest Dscuss real nterest rate Learn annutymmedate, and ts present value Study annutydue, and
More informationIDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS
IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS Chrs Deeley* Last revsed: September 22, 200 * Chrs Deeley s a Senor Lecturer n the School of Accountng, Charles Sturt Unversty,
More informationREQUIRED FOR YEAR END 31 MARCH 2015. Your business information
REQUIRED FOR YEAR END 31 MARCH 2015 Your busness nformaton Your detals Busness detals Busness name Balance date IRD number Contact detals  to ensure our records are up to date, please complete the followng
More informationUnderwriting Risk. Glenn Meyers. Insurance Services Office, Inc.
Underwrtng Rsk By Glenn Meyers Insurance Servces Offce, Inc. Abstract In a compettve nsurance market, nsurers have lmted nfluence on the premum charged for an nsurance contract. hey must decde whether
More information