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 $300,000 (after expenses) per year for 10 years. The cash inflows begin at the end of year 7. At FastTrack, there is a difference of opinion as to the "best" decision rule to use. The four rules under consideration are NPV IRR, Payback Period and Profitability Index (PI) Additional Info: The firm's president has set a maximum acceptable payback period of 8 years for projects and the cost of capital appropriate for this project is 10% Using the end of year cash flows as shown in the table (see below), answer each of the following: Year Cash Flows S0 -$200,000 -$200,000 -$200,000 -$200,000 $200,000 -$200,000 $300,000 $300,000 $300,000 $300,000 $300,000 $300,000 $300,000 $300,000 $300,000 $300,000 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Answer 1

1 a) NPV is found below:

Year	CF	Discount Factor		Discounted CF
0	$   -2,00,000.00	1/(1+0.1)^0=	1	1*-200000=	$   -2,00,000.00
1	$   -2,00,000.00	1/(1+0.1)^1=	0.909090909	0.909090909090909*-200000=	$   -1,81,818.18
2	$   -2,00,000.00	1/(1+0.1)^2=	0.826446281	0.826446280991735*-200000=	$   -1,65,289.26
3	$   -2,00,000.00	1/(1+0.1)^3=	0.751314801	0.751314800901578*-200000=	$   -1,50,262.96
4	$   -2,00,000.00	1/(1+0.1)^4=	0.683013455	0.683013455365071*-200000=	$   -1,36,602.69
5	$   -2,00,000.00	1/(1+0.1)^5=	0.620921323	0.620921323059155*-200000=	$   -1,24,184.26
6	$   -2,00,000.00	1/(1+0.1)^6=	0.56447393	0.564473930053777*-200000=	$   -1,12,894.79
7	$     3,00,000.00	1/(1+0.1)^7=	0.513158118	0.513158118230706*300000=	$     1,53,947.44
8	$     3,00,000.00	1/(1+0.1)^8=	0.46650738	0.466507380209733*300000=	$     1,39,952.21
9	$     3,00,000.00	1/(1+0.1)^9=	0.424097618	0.424097618372485*300000=	$     1,27,229.29
10	$     3,00,000.00	1/(1+0.1)^10=	0.385543289	0.385543289429531*300000=	$     1,15,662.99
11	$     3,00,000.00	1/(1+0.1)^11=	0.350493899	0.350493899481392*300000=	$     1,05,148.17
12	$     3,00,000.00	1/(1+0.1)^12=	0.318630818	0.318630817710357*300000=	$        95,589.25
13	$     3,00,000.00	1/(1+0.1)^13=	0.28966438	0.289664379736688*300000=	$        86,899.31
14	$     3,00,000.00	1/(1+0.1)^14=	0.263331254	0.26333125430608*300000=	$        78,999.38
15	$     3,00,000.00	1/(1+0.1)^15=	0.239392049	0.239392049369163*300000=	$        71,817.61
16	$     3,00,000.00	1/(1+0.1)^16=	0.217629136	0.217629135790149*300000=	$        65,288.74
				NPV = Sum of all Discounted CF	$       -30,517.76

1b) The project should not be selected as the NPV is negative

2a) IRR can be calculated using a financial calculator or excel's goal seek function as it is a hit and trial process. IRR is the discount rate at which the NPV = 0

IRR comes to 9.61% rounded to 2 decimal places

Year	CF	Discount Factor		Discounted CF
0	$   -2,00,000.00	1/(1+0.0960866215040515)^0=	1	1*-200000=	$   -2,00,000.00
1	$   -2,00,000.00	1/(1+0.0960866215040515)^1=	0.912336653	0.912336653309205*-200000=	$   -1,82,467.33
2	$   -2,00,000.00	1/(1+0.0960866215040515)^2=	0.832358169	0.832358168971441*-200000=	$   -1,66,471.63
3	$   -2,00,000.00	1/(1+0.0960866215040515)^3=	0.759390866	0.759390866233983*-200000=	$   -1,51,878.17
4	$   -2,00,000.00	1/(1+0.0960866215040515)^4=	0.692820121	0.69282012145349*-200000=	$   -1,38,564.02
5	$   -2,00,000.00	1/(1+0.0960866215040515)^5=	0.632085191	0.632085190952154*-200000=	$   -1,26,417.04
6	$   -2,00,000.00	1/(1+0.0960866215040515)^6=	0.576674488	0.576674487719599*-200000=	$   -1,15,334.90
7	$     3,00,000.00	1/(1+0.0960866215040515)^7=	0.526121272	0.526121272174899*300000=	$     1,57,836.38
8	$     3,00,000.00	1/(1+0.0960866215040515)^8=	0.479999721	0.479999720690829*300000=	$     1,43,999.92
9	$     3,00,000.00	1/(1+0.0960866215040515)^9=	0.437921339	0.437921338764424*300000=	$     1,31,376.40
10	$     3,00,000.00	1/(1+0.0960866215040515)^10=	0.399531689	0.399531688621022*300000=	$     1,19,859.51
11	$     3,00,000.00	1/(1+0.0960866215040515)^11=	0.364507404	0.364507403687478*300000=	$     1,09,352.22
12	$     3,00,000.00	1/(1+0.0960866215040515)^12=	0.332553465	0.332553464786661*300000=	$        99,766.04
13	$     3,00,000.00	1/(1+0.0960866215040515)^13=	0.303400715	0.303400715109843*300000=	$        91,020.21
14	$     3,00,000.00	1/(1+0.0960866215040515)^14=	0.276803593	0.276803593034934*300000=	$        83,041.08
15	$     3,00,000.00	1/(1+0.0960866215040515)^15=	0.252538064	0.252538063693455*300000=	$        75,761.42
16	$     3,00,000.00	1/(1+0.0960866215040515)^16=	0.230399732	0.230399731863274*300000=	$        69,119.92
				NPV = Sum of all Discounted CF	$                   0.00

2b) As IRR is below 10% the project should not be accepted

3a) Pay back period is calculated below:

Year	Opening Balance	Investment	CF	Closing Balance
0		$      2,00,000.00		$     2,00,000.00
1	$        2,00,000.00		$              -2,00,000.00	$     4,00,000.00
2	$        4,00,000.00		$              -2,00,000.00	$     6,00,000.00
3	$        6,00,000.00		$              -2,00,000.00	$     8,00,000.00
4	$        8,00,000.00		$              -2,00,000.00	$   10,00,000.00
5	$      10,00,000.00		$              -2,00,000.00	$   12,00,000.00
6	$      12,00,000.00		$              -2,00,000.00	$   14,00,000.00
7	$      14,00,000.00		$               3,00,000.00	$   11,00,000.00
8	$      11,00,000.00		$               3,00,000.00	$     8,00,000.00
9	$        8,00,000.00		$               3,00,000.00	$     5,00,000.00
10	$        5,00,000.00		$               3,00,000.00	$     2,00,000.00
11	$        2,00,000.00		$               3,00,000.00	$    -1,00,000.00

Opening balance = previous year's closing balance

Closing balance = Opening balance + investment - CF

We see that the closing balance at year 10 was 200000 while the CF for year 11 was 300000 so during 2/3rd of the year entire investment was recovered so the total payback period is 10 years 8 months

3b) As payback period exceeds the 8 year limit, we should not accept this project

4a)

NPV PI = 1+ CF

PI = 1+- -30,517.76 200000

PI = 0,85

4b) As PI is less than 1 the project should not be invested in

5a) if the required rate doubled to 20% the NPV will fall even further as the required rate is the discount rate:

Discount Factor 0 $ -2,00,000.00 1/(1+0.2)^0= 1 $ -2,00,000.00 1/(1+0.2)^1= 2 $ -2,00,000.00 1/(1+0.2)^2= 3 $ -2,00,000.00 1/(1+0.2)^3= 4 $ -2,00,000.00 1/(1+0.2) 4= 5 $ -2,00,000.00 1/(1+0.2)^5= 6 $ -2,00,000.00 1/(1+0.2)^6= 7 $ 3,00,000.00 1/(1+0.2)^7= 8 $ 3,00,000.00 1/(1+0.2)^8= 9 $ 3,00,000.00 1/(1+0.2) 9= 10 $ 3,00,000.00 1/(1+0.2)^10= 11 $ 3,00,000.00 1/(1+0.2)^11= 12 $ 3,00,000.00 1/(1+0.2)^12= 13 $ 3,00,000.00 1/(1+0.2)^13= 14 $ 3,00,000.00 1/(1+0.2)^14= 15 $ 3,00,000.00 1/(1+0.2)^15= 16 $ 3,00,000.00 1/(1+0.2)^16= Discounted CF 11*-200000= 0.833333333 0.833333333333333*-200000= 0.694444444 0.694444444444444*-200000= 0.578703704 0.578703703703704*-200000= 0.4822530860.482253086419753*-200000= 0.4018775720.401877572016461*-200000= 0.334897977|0.334897976680384*-200000= 0.279081647 0.279081647233653*300000= 0.232568039 0.232568039361378*300000= 0.193806699 0.193806699467815*300000= 0.161505583 0.161505582889846*300000= 0.134587986 0.134587985741538*300000= 0.112156655 0.112156654784615*300000= 0.0934638790.0934638789871793*300000= 0.077886566 0.0778865658226494*300000= 0.064905472 0.0649054715188745*300000= 0.054087893 0.0540878929323954*300000= NPV = Sum of all Discounted CF $ -2,00,000.00 $ -1,66,666.67 $ -1,38,888.89 $ -1,15,740.74 $ -96,450.62 $ -80,375.51 $ -66,979.60 $ 83,724.49 $ 69,770.41 $ 58,142.01 $ 48,451.67 $ 40,376.40 $ 33,647.00 $ 28,039.16 $ 23,365.97 $ 19,471.64 $ 16,226.37 $ -4,43,886.90

If interest rate goes up by 100%, NPV falls by 1355% so for every 1% change in discount rate the NPV changes by 13.55% in the opposite direction

5b) IRR will remain unaffected as it is the discount rate in itself and till the CF dont change, the IRR wont change. If required rate is higher, then we well still not be accepting the project as the IRR is now even lower than the required rate.

5c) Payback period wont be affected as it is an un-discounted measure, had we used a discounted payback period, it would have increased as DCF would be lower leading to a slower recovery.

5d) PI will decrease as NPV will decrease because PI is a derivation of NPV