Question

4. (Prob. 12-14) The following three machines—A, B, and C—are equally risky. Which of these mutually exclusive projects should be accepted at a 12% cost of capital?

Year /Projects	A (cash flow)	B (cash flow)	C (cash flow)
0	-$42,000	-$65,000	-$100,500
1	12,000	10,000	30,000
2	12,000	20,000	30,000
3	12,000	30,000	30,000
4	12,000	40,000	30,000
5	12,000	---	30,000
6	12,000	---	---

1. Which project is accepted, based on the traditional NPV?

NPV(A) =                  ; NPV(B)=                   ; NPV(C)=               ; Accept Project (     );

2. Which project is accepted, based on the annualized NPV (A-NPV)?

A-NPV(A) =                     ; A-NPV(B)=              ; A-NPV(C)=              ; Accept Project (     );

Answer 1

NPV = Present value of Cash Inflows - Present value of cash outlflows

Project A:

Present value at 12%
Present value factor (1/(1+rate)^n	Present value factor	Cash flows	Present value of cash flows
1/(1.12)	0.892857143	12000	10714.28571
1/(1.12)^2	0.797193878	12000	9566.326531
1/(1.12)^3	0.711780248	12000	8541.362974
1/(1.12)^4	0.635518078	12000	7626.216941
1/(1.12)^5	0.567426856	12000	6809.122269
1/(1.12)^6	0.506631121	12000	6079.573454
	4.114	Total Cash Inflow (A)	49336.88788
		Present value of cash outflows (B)	42000
		NPV (A-B)	7336.887882

Project B :

Present value at 12%
Present value factor (1/(1+rate)^n	Present value factor	Cash flows	Present value of cash flows
1/(1.12)	0.892857143	10000	8928.571429
1/(1.12)^2	0.797193878	20000	15943.87755
1/(1.12)^3	0.711780248	30000	21353.40743
1/(1.12)^4	0.635518078	40000	25420.72314
Present value annuity factor	3.0373	Total Cash Inflow (A)	71646.57955
		Present value of cash outflows (B)	65000
		NPV (A-B)	6646.57955

Project C.

Present value at 12%
Present value factor (1/(1+rate)^n	Present value factor	Cash flows	Present value of cash flows
1/(1.12)	0.892857143	30000	26785.71429
1/(1.12)^2	0.797193878	30000	23915.81633
1/(1.12)^3	0.711780248	30000	21353.40743
1/(1.12)^4	0.635518078	30000	19065.54235
1/(1.12)^5	0.567426856	30000	17022.80567
	3.6047	Total Cash Inflow (A)	108143.2861
		Present value of cash outflows (B)	100500
		NPV (A-B)	7643.28607

NPV of project A = 7336.88

project B = 6646.58

Project C = 7643.28

Accept project C

Annualized NPV = NPV / Present value annuity factor ( 12% , number of years)

Project A = 7336.88 / 4.114 ( 4.114 from table 1 )

= $ 1783.39

Project B = 6446.58 / 3.0373 (3.0373 from table 2)

= $ 2122.4706

Project C = 7643.286 / 3.6047

= $ 2120.366

Amoung above three project B has more annualized NPV. which is preferrable.