Question

1. A security is currently selling for $8,000 and promises to pay $1,000 annually for the next 9 years, and $1,500 annually in the 3 years thereafter with all payments occurring at the end of each year. If your required rate of return is 7% p.a., should you buy this security? a. No, because the return is less than 7%.
   2. Yes, because the return is greater than 7%.
   3. Yes, because the return is 7%.
   4. Yes, because the present value at 7% is less than $8,000.
   5. There is insufficient information provided to answer this question.

Answer 1

Let’s compute IRR of the security using trial and error method.

Computation of NPV at discount rate of 8 %.

Year	Cash Flow (C)	Computation of PV Factor	PV Factor @ 8 % (F)	PV (C x F)
0	-$ 8,000	1/ (1+0.08)0	1	-$ 8,000.00
1	$ 1,000	1/ (1+0.08)1	0.92592592592593	$ 925.925926
2	$ 1,000	1/ (1+0.08)2	0.85733882030178	$ 857.338820
3	$ 1,000	1/ (1+0.08)3	0.79383224102017	$ 793.832241
4	$ 1,000	1/ (1+0.08)4	0.73502985279645	$ 735.029853
5	$ 1,000	1/ (1+0.08)5	0.68058319703375	$ 680.583197
6	$ 1,000	1/ (1+0.08)6	0.63016962688311	$ 630.169627
7	$ 1,000	1/ (1+0.08)7	0.58349039526213	$ 583.490395
8	$ 1,000	1/ (1+0.08)8	0.54026888450198	$ 540.268885
9	$ 1,000	1/ (1+0.08)9	0.50024896713146	$ 500.248967
10	$ 1,500	1/ (1+0.08)10	0.46319348808468	$ 694.790232
11	$ 1,500	1/ (1+0.08)11	0.42888285933767	$ 643.324289
12	$ 1,500	1/ (1+0.08)12	0.39711375864599	$ 595.670638
			NPV1	$ 180.67307

As NPV is negative let’s compute NPV at discount rate of 9 %.

Year	Cash Flow (C)	Computation of PV Factor	PV Factor @ 9 % (F)	PV (C x F)
0	-$ 8,000	1/ (1+0.09)0	1	-$ 8,000.0000
1	$ 1,000	1/ (1+0.09)1	0.91743119266055	$ 917.431193
2	$ 1,000	1/ (1+0.09)2	0.84167999326656	$ 841.679993
3	$ 1,000	1/ (1+0.09)3	0.77218348006106	$ 772.183480
4	$ 1,000	1/ (1+0.09)4	0.70842521106520	$ 708.425211
5	$ 1,000	1/ (1+0.09)5	0.64993138629835	$ 649.931386
6	$ 1,000	1/ (1+0.09)6	0.59626732687922	$ 596.267327
7	$ 1,000	1/ (1+0.09)7	0.54703424484332	$ 547.034245
8	$ 1,000	1/ (1+0.09)8	0.50186627967277	$ 501.866280
9	$ 1,000	1/ (1+0.09)9	0.46042777951630	$ 460.427780
10	$ 1,500	1/ (1+0.09)10	0.42241080689569	$ 633.616210
11	$ 1,500	1/ (1+0.09)11	0.38753285036302	$ 581.299276
12	$ 1,500	1/ (1+0.09)12	0.35553472510369	$ 533.302088
			NPV2	-$ 256.535531

IRR = R1 + [NPV1 x (R2 – R1)/ (NPV1 – NPV2)]

= 8 % + [$ 180.67307 x (9 % - 8 %)/ ($ 180.67307– (-$ 256.535531))]

= 8 % + [($ 180.67307 x 1 %)/ ($ 180.67307 + $ 256.535531)]

= 8 % + ($ 1.8067307/ $ 437.208601)

= 8 % + 0.004132423

= 8 % + 0.41 % = 8.41 %

Security should be purchased as the rate of return, 8.41 % is higher than required rate of return.

Option “Yes, because the return is greater than 7 %” is correct answer.