Question

His recently departed Uncle Jimmy, may he rest in peace, has left Scott a 15-year annuity (15 annual payments). He will receive the first payment of $8,000 in 5 years from today, and payments will grow at a constant rate of 3% per year thereafter. If he is discounting at 6% (EAR), what is the present value of his inheritance?

Select one:

a. $73,911

b. $93,311

c. $69,727

d. $61,544

e. $127,530

f. $69,911

g. $98,909

h. No solution since r>g

NOTE: Please show all the work, without using EXCEL (Step by step with equations) Thanks!

Answer 1

Payment of $8000 will be received in 5 years from now. This mean the first cash flow will received at the end of 5th year.

So he will receive total 15 payments up to end of 19th year. Payments will grow at the rate 3% constantly every year.

The following table shows the cash flows in today terms:

Year (1)	Receipt (2)	PVF* @6% (3)	Receipt*PVF* (4) = (2)*(3)
1	0	0.943396	0
2	0	0.889996	0
3	0	0.839619	0
4	0	0.792094	0
5	8000	0.747258	5978.065
6	(8000*103%) = 8240	0.704961	5808.875
7	(8240*103%) = 8487.20	0.665057	5644.473
8	(8487.20*103%) = 8741.82	0.627412	5484.726
9	(8741.82*103%) = 9004.07	0.591898	5329.495
10	(9004.07*103%) = 9274.19	0.558395	5178.659
11	(9274.19*103%) = 9552.42	0.526788	5032.096
12	(9552.42*103%) = 9838.99	0.496969	4889.677
13	(9838.99*103%) = 10134.16	0.468839	4751.29
14	(10134.16*103%) = 10438.19	0.442301	4616.817
15	(10438.19*103%) = 10751.33	0.417265	4486.154
16	(10751.33*103%) = 11073.87	0.393646	4359.188
17	(11073.87*103%) = 11406.09	0.371364	4235.816
18	(11406.09*103%) = 11748.27	0.350344	4115.933
19	(11748.27*103%) = 12100.72	0.330513	3999.445
			73910.71

* PVF = Present Value Factor

The Present Value of Inheritence is $73911. The answer is Option 'a'.