# 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 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)

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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