Question

FastTrack​ Bikes, Inc. is thinking of developing a new composite road bike. Development will take six years and the cost is

$ 200 comma 000$200,000

per year. Once in​ production, the bike is expected to make

$ 300 comma 000$300,000

per year for

1010

years. The cash inflows begin at the end of year 7.

For parts​ a-c, assume the cost of capital is

10.0 %10.0%.

a. Calculate the NPV of this investment opportunity. Should the company make the​ investment?

b. Calculate the IRR and use it to determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged.

c. How long must development last to change the​ decision?

For parts​ d-f, assume the cost of capital is

14.0 %14.0%.

d. Calculate the NPV of this investment opportunity. Should the company make the​ investment?

e. How much must this cost of capital estimate deviate to change the​ decision?

f. How long must development last to change the​ decision?

Answer 1

CALCULATION OF NPV, IRR AND OTHER CAPITAL BUDGETING RELATED ANALYSIS: -

a. CALCULATION OF NPV

NPV is present value of future cashflows discounted at the desired rate of return.

Year	Cash flows	Present value @10%
1	-2,00,000	-1,81,818
2	-2,00,000	-1,65,289
3	-2,00,000	-1,50,263
4	-2,00,000	-1,36,603
5	-2,00,000	-1,24,184
6	-2,00,000	-1,12,895
7	3,00,000	1,53,947
8	3,00,000	1,39,952
9	3,00,000	1,27,229
10	3,00,000	1,15,663
11	3,00,000	1,05,148
12	3,00,000	95,589
13	3,00,000	86,899
14	3,00,000	78,999
15	3,00,000	71,818
16	3,00,000	65,289

Present value is calclulated as Cashflow/ (1 + rt) where r is rate of return, t is time period of cashflow. Example, for year 2 discounted cashflow is calculated as -$2,00,000 / ( 1 + 0.10)2

Summing up all discounted cashflows gives NPV of $1,69,482

YES COMPANY SHOULD ACCEPT THE PROPOSAL AND MAKE INVESTMENT AS NPV IS 1,69,482 i.e. company will earn its desired rate of return and in addition to that, it will also earn $1,69,482.

b. CALCULATION OF IRR

IRR is rate of return at which sum of present value of cash inflows is equal to cashoutflows.

We will calculate IRR using extrapolation method as follows: -

IRR = Lower rate + (NPV at higher rate/ NPV at higher rate - NPV at lower rate) x difference of rate.

Now let the lower rate by 10%, NPV at lower rate = 1,69,482

Let the higher rate be 14%, NPV is as follows: -

Year	Cash flows	Present value @14%
1	-2,00,000	-1,75,439
2	-2,00,000	-1,53,894
3	-2,00,000	-1,34,994
4	-2,00,000	-1,18,416
5	-2,00,000	-1,03,874
6	-2,00,000	-91,117
7	3,00,000	1,19,891
8	3,00,000	1,05,168
9	3,00,000	92,252
10	3,00,000	80,923
11	3,00,000	70,985
12	3,00,000	62,268
13	3,00,000	54620.81
14	3,00,000	47,913
15	3,00,000	42,029
16	3,00,000	36,967
	-64,816

Therefore NPV at 14% is -$64,816

Now IRR = 10% + [(-64,816) / ( -64,816 - 1,69,482)] x (14% - 10%)

=>IRR = 10% + [-64,816/ -(2,34,298)] x 4%

=>IRR = 10% + (0.276639 x 4%)

=>IRR = 10% + 1.10656

=>IRR = 11.10656%

Maximum deviation allowed in cost of capital to remian decision unchanged is 1.10656% i.e. approx 1.10% addition will bring NPV to 0 and further addtion will lead to negative NPV and hence change of decision.

c. CALCULATION OF YEARS OF DEVELOPMENT FOR CHANGING DECISION

This part is basically requires number of years development cost should last for change in decision. We need to identify it on hit and trial method.

1. Assuming development cost will last for 7 years and cash inflows will be starting from end of eight year, leets calculate NPV with same cashflows(Rate of return used is 10% only) Rest all facts remain same.

Year	Cash flows	Present value @10%
1	-2,00,000	-1,81,818
2	-2,00,000	-1,65,289
3	-2,00,000	-1,50,263
4	-2,00,000	-1,36,603
5	-2,00,000	-1,24,184
6	-2,00,000	-1,12,895
7	-2,00,000	-1,02,632
8	3,00,000	1,39,952
9	3,00,000	1,27,229
10	3,00,000	1,15,663
11	3,00,000	1,05,148
12	3,00,000	95,589
13	3,00,000	86,899
14	3,00,000	78,999
15	3,00,000	71,818
16	3,00,000	65,289
17	3,00,000	59,353
NPV	-27,743

THEREFORE BY INCREASING DEVELOPMENT COST BY ONE YEAR i.e. year 7, NPV of proposal turns out to be negative -$27,743. Therefore 1 year increase in development cost will lead to change of investment devision.

d. CALCULATION OF NPV WITH 14% COST OF CAPITAL

NPV WILL BE CALCUATED ON SIMILAR MANNER WITH DISCOUNTING RATE AS 14%

Year	Cash flows	Present value @14%
1	-2,00,000	-1,75,439
2	-2,00,000	-1,53,894
3	-2,00,000	-1,34,994
4	-2,00,000	-1,18,416
5	-2,00,000	-1,03,874
6	-2,00,000	-91,117
7	3,00,000	1,19,891
8	3,00,000	1,05,168
9	3,00,000	92,252
10	3,00,000	80,923
11	3,00,000	70,985
12	3,00,000	62,268
13	3,00,000	54620.81
14	3,00,000	47,913
15	3,00,000	42,029
16	3,00,000	36,967
NPV	-64,816

THEREFORE NPV AT 14% COST OF CAPITAL WILL BE -$64,816.

SINCE NPV IS NEGATIVE AND COMPANY IS NOT ABLE TO EXTRACT ITS COST OF CAPITAL i.e. 14%, investment should not be done and proposal should be rejected.

PLEASE NOTE THAT IN ABSENCE OF SPECIFIC REQUIREMENT ASKED BY STUDENT, I AM SOLVING ONLY FIRST FOUR SUBPARTS OF THIS QUESTION.