Exercise 6 8. Exercise 6 12 PVA = $5,000 x * = $21,776

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Kory Mathews
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1 CHAPTER 6: EXERCISES Exercise FV = $10,000 ( * ) = $26,533 * Future value of $1: n = 20, i = 5% (from Table 1) 2. FV = $10,000 ( * ) = $18,061 * Future value of $1: n = 20, i = 3% (from Table 1) 3. FV = $10,000 ( * ) = $18,114 * Future value of $1: n = 30, i = 2% (from Table 1) Exercise 6 4 PV of $1 Payment i=8% PV n First payment: $5,000 x = $ 4,630 1 Second payment 6,000 x = 5,144 2 Third payment 8,000 x = 5,880 4 Fourth payment 9,000 x = 5,672 6 Total $21,326 Exercise FVA = $2,000 (4.7793* ) = $9,559 * Future value of an ordinary annuity of $1: n = 4, i = 12% (from Table 3) 2. FVAD = $2,000 (5.3528* ) = $10,706 * Future value of an annuity due of $1: n = 4, i = 12% (from Table 5) 3. FV of $1 Deposit i=3% FV n First deposit: $2,000 x = $ 3, Second deposit 2,000 x = 2, Third deposit 2,000 x = 2,534 8 Fourth deposit 2,000 x = 2,251 4 Total $10, $2,000 x 4 = $8,000

81136 * ) = $18,114 * Future value of $1: n = 30, i = 2% (from Table 1) Exercise 6 4 PV of $1 Payment i=8% PV n First payment: $5,000 x.92593 = $ 4,630 1 Second payment 6,000 x.

2 Exercise PVA = $5,000 ( * ) = $18,024 * Present value of an ordinary annuity of $1: n = 5, i = 12% (from Table 4) 2. PVAD = $5,000 ( * ) = $20,187 * Present value of an annuity due of $1: n = 5, i =12% (from Table 6) 3. PV of $1 Payment i = 3% PV n First payment: $5,000 x = $ 4,442 4 Second payment 5,000 x = 3,947 8 Third payment 5,000 x = 3, Fourth payment 5,000 x = 3, Fifth payment 5,000 x = 2, Total $17,780 Exercise Choose the option with the highest present value. (1) PV = $64,000 (2) PV = $20, ,000 ( * ) * Present value of an ordinary annuity of $1: n = 6, i = 6% (from Table 4) PV = $20, ,339 = $59,339 (3) PV = $13,000 ( * ) = $63,925 Alex should choose option (1). 2. FVA = $100,000 ( * ) = $1,381,640 * Future value of an ordinary annuity of $1: n = 10, i = 7% (from Table 3) Exercise 6 12 PVA = $5,000 x * = $21,776

78941 = 3,947 8 Third payment 5,000 x.70138 = 3,507 12 Fourth payment 5,000 x.62317 = 3,116 16 Fifth payment 5,000 x.55368 = 2,768 20 Total $17,780 Exercise 6 11 1.

3 * Present value of an ordinary annuity of $1: n = 6, i = 10% (from Table 4) PV = $21,776 x.82645* = $17,997 * Present value of $1: n = 2, i = 10% (from Table 2) Or alternatively: From Table 4, PVA factor, n = 8, i = 10% = PVA factor, n = 2, i = 10% = = PV factor for deferred annuity = PV = $5,000 x = $17,997 Exercise 6 17 To determine the price of the bonds, we calculate the present value of the 40- period annuity (40 semiannual interest payments of $12 million) and the lump-sum payment of $300 million paid at maturity using the semiannual market rate of interest of 5%. In equation form, PV = $12,000,000 1 ( * ) + 300,000,000 (.14205** ) PV = $205,909, ,615,000 = $248,524,080 = price of the bonds 1 $300,000,000 x 4 % = $12,000,000 * Present value of an ordinary annuity of $1: n = 40, i = 5% (from Table 4) ** Present value of $1: n = 40, i = 5% (from Table 2) Exercise 6 19 Requirement 1 PVA = $400,000 ( * ) = $4,237,604 = Liability * Present value of an ordinary annuity of $1: n = 20, i = 7% (from Table 4) Requirement 2 PVAD = $400,000 ( * ) = $4,534,240 = Liability * Present value of an annuity due of $1: n = 20, i = 7% (from Table 6)

73554 = PV factor for deferred annuity = 3.59939 PV = $5,000 x 3.

4 PROBLEMS Problem 6 1 Choose the option with the lowest present value of cash outflows, net of the present value of any cash inflows (Cash outflows are shown as negative amounts; cash inflows as positive amounts). Machine A: PV = $48,000 1,000 ( * ) + 5,000 (.46319** ) * Present value of an ordinary annuity of $1: n = 10, i = 8% (from Table 4) ** Present value of $1: n = 10, i = 8% (from Table 2) PV = $48,000 6,710 + $2,316 PV = $52,394 Machine B: PV = $40,000 4,000 (.79383) 5,000 (.63017) 6,000 (.54027) PV of $1: i = 8% n = 3 n = 6 n = 8 (from Table 2) PV = $40,000 3,175 3,151 3,242 PV = $49,568 Esquire should purchase machine B. Problem PV = $10, ,000 ( * ) = $40,326 = Equipment * Present value of an ordinary annuity of $1: n = 5, i = 10% (from Table 4) 2. $400,000 = Annuity amount x * * Future value of an annuity due of $1: n = 5, i = 6% (from Table 5) Annuity amount = $400, Annuity amount = $66,942 = Required annual deposit 3. PVAD = $120,000 ( * ) = $1,123,790 = Lease liability * Present value of an annuity due of $1: n = 20, i = 10% (from Table 6)

46319** ) * Present value of an ordinary annuity of $1: n = 10, i = 8% (from Table 4) ** Present value of $1: n = 10, i = 8% (from Table 2) PV = $48,000 6,710 + $2,316 PV = $52,394 Machine B: PV =

5 Problem 6 3 Choose the option with the lowest present value of cash payments. 1. PV = $1,000, PV = $420, ,000 ( * ) = $956,806 * Present value of an ordinary annuity of $1: n = 10, i = 8% (from Table 4) 3. PV = PVAD = $135,000 ( * ) = $978,330 * Present value of an annuity due of $1: n = 10, i = 8% (from Table 6) 4. PV = $1,500,000 (.68058* ) = $1,020,870 * Present value of $1: n = 5, i = 8% (from Table 2) Harding should choose option 2. Problem 6 4 The restaurant should be purchased if the present value of the future cash flows discounted at a 10% rate is greater than $800,000. PV = $80,000 ( * ) + 70,000 (.51316** ) + 60,000 (.46651**) n = 7 n = ,000 (.42410**) + 40,000 (.38554**) + 700,000 (.38554**) n = 9 n = 10 n = 10 * Present value of an ordinary annuity of $1: n = 6, i = 10% (from Table 4) ** Present value of $1: i = 10% (from Table 2) PV = $718,838 < $800,000 Since the PV is less than $800,000, the restaurant should not be purchased.

24689* ) = $978,330 * Present value of an annuity due of $1: n = 10, i = 8% (from Table 6) 4. PV = $1,500,000 (.

6 Problem 6 5 The maximum amount that should be paid for the store is the present value of the estimated cash flows. Years 1 5: PVA = $70,000 x * = $279,490 * Present value of an ordinary annuity of $1: n = 5, i = 8% (from Table 4) Years 6 10: PVA = $70,000 x * = $265,355 * Present value of an ordinary annuity of $1: n = 5, i = 10% (from Table 4) PV = $265,355 x.68058* = $180,595 * Present value of $1: n = 5, i = 8% (from Table 2) Years 11 20: PVA = $70,000 x * = $395,515 * Present value of an ordinary annuity of $1: n = 10, i = 12% (from Table 4) PV = $395,515 x.62092* = $245,583 * Present value of $1: n = 5, i = 10% (from Table 2) PV = $245,583 x.68058* = $167,139 * Present value of $1: n = 5, i = 8% (from Table 2) End of Year 20: PV = $400,000 x.32197* x x = $54,424 * Present value of $1: n = 10, i = 12% (from Table 2) Total PV = $279, , , ,424 = $681,648 The maximum purchase price is $681,648.

79079* = $265,355 * Present value of an ordinary annuity of $1: n = 5, i = 10% (from Table 4) PV = $265,355 x.

7 Problem 6 13 Choose the option with the lowest present value of cash outflows, net of the present value of any cash inflows. (Cash outflows are shown as negative amounts; cash inflows as positive amounts) 1. Buy option: PV = $160,000 5,000 ( * ) + 10,000 (.32197** ) * Present value of an ordinary annuity of $1: n = 10, i = 12% (from Table 4) ** Present value of $1: n = 10, i = 12% (from Table 2) PV = $160,000 28, ,220 PV = $185, Lease option: PVAD = $25,000 ( * ) = $158,206 * Present value of an annuity due of $1: n = 10, i = 12% (from Table 6) Kiddy Toy should lease the machine.

32197** ) * Present value of an ordinary annuity of $1: n = 10, i = 12% (from Table 4) ** Present value of $1: n = 10, i = 12% (from Table 2) PV =

Time Value of Money. 15.511 Corporate Accounting Summer 2004. Professor S. P. Kothari Sloan School of Management Massachusetts Institute of Technology

Time Value of Money. 15.511 Corporate Accounting Summer 2004. Professor S. P. Kothari Sloan School of Management Massachusetts Institute of Technology Time Value of Money 15.511 Corporate Accounting Summer 2004 Professor S. P. Kothari Sloan School of Management Massachusetts Institute of Technology July 2, 2004 1 LIABILITIES: Current Liabilities Obligations