Question

FastTrack​ Bikes, Inc. is thinking of developing a new composite road bike. Development will take six years and the cost is $ 200 000 per year. Once in​ production, the bike is expected to make $ 300000 per year for 10 years. Assume the cost of capital is 10 %.

a. Calculate the NPV of this investment​ opportunity, assuming all cash flows occur at the end of each year. Should the company make the​ investment

present value of costs is ______

present value of benefits is _________

the NPV is _________

b. By how much must the cost of capital estimate deviate to change the​ decision?​ (Hint: Use Excel to calculate the​ IRR.)

to change the decison, the deviation would need to be _____%

c. What is the NPV of the investment if the cost of capital is 14 %​? ​Note: Assume that all cash flows occur at the end of the appropriate year and that the inflows do not start until year 7.

The Present value of the costs is ____________

The present value of benefits is ____________

the NPV will be___________

Answer 1

NPV is the difference between present values of cash inflow and outflow.

NPV = PV of Cash Inflow - PV of Cash Outflow

Year	CF(a)	PVF(b)	PV(a*b)
1	-200000	0.91	-181818.18
2	-200000	0.83	-165289.26
3	-200000	0.75	-150262.96
4	-200000	0.68	-136602.69
5	-200000	0.62	-124184.26
6	-200000	0.56	-112894.79
7	300000	0.51	153947.44
8	300000	0.47	139952.21
9	300000	0.42	127229.29
10	300000	0.39	115662.99
11	300000	0.35	105148.17
12	300000	0.32	95589.25
13	300000	0.29	86899.31
14	300000	0.26	78999.38
15	300000	0.24	71817.61
16	300000	0.22	65288.74
	NPV		169482.24

PV of Cost = -871052.14

PV of Benefit = 1040534.38

Here NPV is Positive. To change our decision NPV should be either 0 or negative.

IRR is the point where NPV is 0

To calculate IRR we will use hit and trial method.

NPV @ 12%

Year	CF(a)	PVF(b)	PV(a*b)
1	-200000	0.89	-178571.43
2	-200000	0.80	-159438.78
3	-200000	0.71	-142356.05
4	-200000	0.64	-127103.62
5	-200000	0.57	-113485.37
6	-200000	0.51	-101326.22
7	300000	0.45	135704.76
8	300000	0.40	121164.97
9	300000	0.36	108183.01
10	300000	0.32	96591.97
11	300000	0.29	86242.83
12	300000	0.26	77002.53
13	300000	0.23	68752.26
14	300000	0.20	61385.94
15	300000	0.18	54808.88
16	300000	0.16	48936.50
	Total		36492.18

NPV @ 13%

Year	CF(a)	PVF(b)	PV(a*b)
1	-200000	0.88	-176991.15
2	-200000	0.78	-156629.34
3	-200000	0.69	-138610.03
4	-200000	0.61	-122663.75
5	-200000	0.54	-108551.99
6	-200000	0.48	-96063.71
7	300000	0.43	127518.19
8	300000	0.38	112847.96
9	300000	0.33	99865.45
10	300000	0.29	88376.50
11	300000	0.26	78209.30
12	300000	0.23	69211.77
13	300000	0.20	61249.35
14	300000	0.18	54202.97
15	300000	0.16	47967.23
16	300000	0.14	42448.87
	Total		-17612.38

IRR = lower rate + [(lower rate NPV *(Higher Rate - Lower Rate))/(Lowe rate NPV- Higher Rate NPV]

= 12% +[(36492*(13-12))/(36492+17612) = 12.67%

Calculating in Excel

Year	CF(a)
1	-200000
2	-200000
3	-200000
4	-200000
5	-200000
6	-200000
7	300000
8	300000
9	300000
10	300000
11	300000
12	300000
13	300000
14	300000
15	300000
16	300000
IRR	12.66%

Hence Confirmed.

Current Discount Rate = 10%

IRR = 12.66%

Deviation = 2.66/10 = 26.67%

NPV @ 14%

Year	CF(a)	PVF(b)	PV(a*b)
1	-200000	0.88	-175438.60
2	-200000	0.77	-153893.51
3	-200000	0.67	-134994.30
4	-200000	0.59	-118416.06
5	-200000	0.52	-103873.73
6	-200000	0.46	-91117.31
7	300000	0.40	119891.20
8	300000	0.35	105167.72
9	300000	0.31	92252.38
10	300000	0.27	80923.14
11	300000	0.24	70985.21
12	300000	0.21	62267.73
13	300000	0.18	54620.82
14	300000	0.16	47913.00
15	300000	0.14	42028.94
16	300000	0.12	36867.50
	NPV		-64815.87

PV of Cost = -777733.5

PV of Benefit = 712917.64