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


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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
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
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 lumpsum 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)
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)
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.
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.
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.
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