Question

Violet Sky Consulting has a weighted-average cost of capital of 9.46 percent and is evaluating two projects: A and B. Project A involves an initial investment of 6,723 dollars and an expected cash flow of 9,748 dollars in 8 years. Project A is considered more risky than an average-risk project at Violet Sky Consulting, such that the appropriate discount rate for it is 1.21 percentage points different than the discount rate used for an average-risk project at Violet Sky Consulting. The internal rate of return for project A is 4.75 percent. Project B involves an initial investment of 4,242 dollars and an expected cash flow of 7,211 dollars in 9 years. Project B is considered less risky than an average-risk project at Violet Sky Consulting, such that the appropriate discount rate for it is 1.28 percentage points different than the discount rate used for an average-risk project at Violet Sky Consulting. The internal rate of return for project B is 6.07 percent. What is X if X equals the NPV of project A plus the NPV of project B?

Answer 1

Formula sheet

A	B	C	D	E	F	G	H	I	J	K	L	M	N
2
3		WACC for the firm	0.0946
4		Cost of capital of project A	=D3+1.21%
5		Cost of capital of project B	=D3-1.28%
6
7		Cash Flow of project A will be as follows:
8		Year	0	1	2	3	4	5	6	7	8
9		Cash Flow	-6723	9748	=$E$9	=$E$9	=$E$9	=$E$9	=$E$9	=$E$9	=$E$9
10
11		Cash Flow of project B will be as follows:
12		Year	0	1	2	3	4	5	6	7	8	9
13		Cash Flow	-4242	7211	=E13	=F13	=G13	=H13	=I13	=J13	=K13	=L13
14
15		Calculation of NPV of project A:
16
17		NPV of the project is present value of future cash flows discounted at required rate of return less the initial investment.
18
19		Year	0	1	2	3	4	5	6	7	8
20		Cash Flow (FCF)	=D9	=E9	=F9	=G9	=H9	=I9	=J9	=K9	=L9
21		Cost of capital (i)	=D4
22		(P/F,i,n) for each year		=1/((1+$D21)^E19)	=1/((1+$D21)^F19)	=1/((1+$D21)^G19)	=1/((1+$D21)^H19)	=1/((1+$D21)^I19)	=1/((1+$D21)^J19)	=1/((1+$D21)^K19)	=1/((1+$D21)^L19)
23		Present Value of cash flows = FCF*(P/F,i,n)		=E20*E22	=F20*F22	=G20*G22	=H20*H22	=I20*I22	=J20*J22	=K20*K22	=L20*L22
24		Present value if future cash flows	=SUM(E23:L23)	=SUM(E23:L23)
25
26		NPV for Project	=Present value fo future cash flows - Initial investment
27			=D24+D20	=D24+D20
28
29		Hence NPV for Project A	=D27
30
31		Calculation of NPV of project B:
32
33		NPV of the project is present value of future cash flows discounted at required rate of return less the initial investment.
34		Given the following cash flow and WACC, NPV for the project can be calculated as follows:
35		Year	0	1	2	3	4	5	6	7	8	9
36		Cash Flow (FCF)	=D13	=E13	=F13	=G13	=H13	=I13	=J13	=K13	=L13	=M13
37		Cost of capital (i)	=D5
38		(P/F,i,n) for each year		=1/((1+$D37)^E35)	=1/((1+$D37)^F35)	=1/((1+$D37)^G35)	=1/((1+$D37)^H35)	=1/((1+$D37)^I35)	=1/((1+$D37)^J35)	=1/((1+$D37)^K35)	=1/((1+$D37)^L35)	=1/((1+$D37)^M35)
39		Present Value of cash flows = FCF*(P/F,i,n)		=E36*E38	=F36*F38	=G36*G38	=H36*H38	=I36*I38	=J36*J38	=K36*K38	=L36*L38	=M36*M38
40		Present value if future cash flows	=SUM(E39:M39)	=SUM(E39:M39)
41
42		NPV for Project	=Present value fo future cash flows - Initial investment
43			=D40+D36	=D40+D36
44
45		Hence NPV for Project B	=D43
46
47		Value of X	=NPV of Project A + NPV of Project B
48			=D29+D45	=D29+D45
49
50		Thus Value of X is	=D48
51