Question

The King Corporation has two alternative projects for producing and marketing video game. Project A requires an initial outlay of $213,000 and will generate annual cash flows of $53,000 for 20-years. Project B requires an initial outlay of $322,000, but will generate annual cash flows of $62,000 for 20 years. It is estimated that both projects have no salvage value at the end of year 20. Firm’s RRR is 9% and the annual cash flows on both projects are already include depreciation and taxes each year. Using the given information, answer the following questions.

a. Find the NPV of project A.
b. Find the NPV of project B.
c. What is the difference of two NPVs?
d. If two projects have same NPV (that is, the difference of two NPVs is zero), what is the Firm’s RRR?​

	Project A	Project B
Intial Outlay
Annaual Net Cash Flow
RRR both projects
Year	Project A	Project B
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
NPV
Difference

Answer 1

Discount rate	9.0000%
Cash flows	Year	Discounted CF= cash flows/(1+rate)^year	Cumulative cash flow
(213,000.000)	0	(213,000.00)	(213,000.00)
53,000.000	1	48,623.85	(164,376.15)
53,000.000	2	44,609.04	(119,767.107)
53,000.000	3	40,925.72	(78,841.38)
53,000.000	4	37,546.54	(41,294.85)
53,000.000	5	34,446.36	(6,848.48)
53,000.000	6	31,602.17	24,753.69
53,000.000	7	28,992.81	53,746.50
53,000.000	8	26,598.91	80,345.41
53,000.000	9	24,402.67	104,748.09
53,000.000	10	22,387.77	127,135.86
53,000.000	11	20,539.24	147,675.10
53,000.000	12	18,843.34	166,518.44
53,000.000	13	17,287.47	183,805.91
53,000.000	14	15,860.06	199,665.97
53,000.000	15	14,550.52	214,216.49
53,000.000	16	13,349.10	227,565.58
53,000.000	17	12,246.88	239,812.46
53,000.000	18	11,235.67	251,048.13
53,000.000	19	10,307.95	261,356.08
53,000.000	20	9,456.84	270,812.92

NPV of A = 270,812.92

Discount rate	9.0000%
Cash flows	Year	Discounted CF= cash flows/(1+rate)^year	Cumulative cash flow
(322,000.000)	0	(322,000.00)	(322,000.00)
62,000.000	1	56,880.73	(265,119.27)
62,000.000	2	52,184.16	(212,935.106)
62,000.000	3	47,875.38	(165,059.73)
62,000.000	4	43,922.36	(121,137.37)
62,000.000	5	40,295.75	(80,841.62)
62,000.000	6	36,968.57	(43,873.05)
62,000.000	7	33,916.12	(9,956.92)
62,000.000	8	31,115.71	21,158.79
62,000.000	9	28,546.52	49,705.31
62,000.000	10	26,189.47	75,894.78
62,000.000	11	24,027.04	99,921.81
62,000.000	12	22,043.15	121,964.97
62,000.000	13	20,223.08	142,188.04
62,000.000	14	18,553.28	160,741.32
62,000.000	15	17,021.36	177,762.68
62,000.000	16	15,615.93	193,378.61
62,000.000	17	14,326.54	207,705.14
62,000.000	18	13,143.61	220,848.76
62,000.000	19	12,058.36	232,907.12
62,000.000	20	11,062.72	243,969.83

NPV of B = 243,969.83

differential cash flow = cash flow B - Cash flow A

Discount rate	5.3395%
Cash flows	Year	Discounted CF= cash flows/(1+rate)^year	Cumulative cash flow
(109,000.000)	0	(109,000.00)	(109,000.00)
9,000.000	1	8,543.80	(100,456.20)
9,000.000	2	8,110.73	(92,345.465)
9,000.000	3	7,699.61	(84,645.85)
9,000.000	4	7,309.33	(77,336.53)
9,000.000	5	6,938.83	(70,397.70)
9,000.000	6	6,587.11	(63,810.58)
9,000.000	7	6,253.22	(57,557.36)
9,000.000	8	5,936.25	(51,621.11)
9,000.000	9	5,635.35	(45,985.76)
9,000.000	10	5,349.71	(40,636.05)
9,000.000	11	5,078.54	(35,557.51)
9,000.000	12	4,821.11	(30,736.40)
9,000.000	13	4,576.74	(26,159.66)
9,000.000	14	4,344.75	(21,814.90)
9,000.000	15	4,124.52	(17,690.38)
9,000.000	16	3,915.46	(13,774.92)
9,000.000	17	3,716.99	(10,057.94)
9,000.000	18	3,528.58	(6,529.36)
9,000.000	19	3,349.72	(3,179.63)
9,000.000	20	3,179.93	0.30

Use IRR funciton in Excel

RR at which the NPV would be same = 5.34%