Question

Consider the following cash flows of two mutually exclusive projects for AZ-Motorcars.

  

YEAR	AZM MINI-SUV	AZF FULL-SUV
0	–$309,671	–$29,559
1	25,500	12,458
2	57,000	9,218
3	50,000	10,390
4	394,000	12,479

  

Whichever project you choose, if any, you require a 15 percent return on your investment.

  

a.	The payback period for Projects A and B is ____ and ____ years, respectively. (Round your answers to 2 decimal places. (e.g., 32.16))

  

b.	The NPV for Projects A and B is $____ and $_____ , respectively. (Round your answers to 2 decimal places, (e.g., 32.16))

  

c.	The IRR for Projects A and B is ____ percent and ____ percent ,respectively. (Round your answers to 2 decimal places. (e.g., 32.16))

Answer 1

a) The payback period for Project A and B is to be calculated as follows:

YEAR	AZM MINI-SUV (Project A)
0	-$3,09,671
1	$25,500
2	$57,000
3	$50,000
4	$3,94,000

Initial Cash Outlay = $3,09,671

Since, the cash inflows are uneven, therefore formulae for calculating the payback period,

Payback period = Year prior to full recovery + Unrecovered cash flow at the beginning of the year / Cash flow during the year

Initial Investment = $3,09,671
Year	Cash inflow	Cumulative Cash inflows
1	$25,500	$25,500
2	$57,000	$82,500
3	$50,000	$1,32,500
4	$3,94,000	$5,26,500

Payback period = 3.45 years

YEAR	AZF FULL-SUV (Project B)
0	-$29,559
1	$12,458
2	$9,218
3	$10,390
4	$12,479

Initial Cash Outlay = $29,559

Initial Investment = $29,559
Year	Cash inflow	Cumulative Cash inflows
1	$12,458	12,458
2	$9,218	21,676
3	$10,390	32,066
4	$12,479	44,545

Payback period = 2.76 years

Therefore, the payback period for Project A and B is 3.45 and 2.76 years, respectively

b)The NPV for project A and B is to be calculated as follows:

NPV = Cash inflow / (1+r)^t - Initial investment,

where,

r = Required return or discount rate

t = Number of time periods

Project A

NPV = 25500/(1+0.15)¹ + 57000/(1+0.15)² + 50000/(1+0.15)³ + 394000/(1+0.15)⁴ - 309671

NPV = $11,956

Project B

NPV = 12458/(1+0.15)¹ + 9218/(1+0.15)² + 10390/(1+0.15)³ + 12479/(1+0.15)⁴ - 29559

NPV = $1,922

Therefore, the NPV for Project A and B is $11,956 and $1,922, respectively

c) The IRR for Project A and B is to be calculated as follows:

IRR = NPV = Cash inflow / (1+r)^t - Initial investment = 0,

In other words, IRR is a point where NPV of a project is zero.

Project A

IRR = 25500/(1+0.15)¹ + 57000/(1+0.15)² + 50000/(1+0.15)³ + 394000/(1+0.15)⁴ - 309671

IRR = 16.47%

Project B

IRR = 12458/(1+0.15)¹ + 9218/(1+0.15)² + 10390/(1+0.15)³ + 12479/(1+0.15)⁴ - 29559

IRR = 18.66%

Therefore, the IRR for Project A and B is 16.47 percent and 18.66 percent, respectively.

Based on the above analysis, Project B would be chosen due to its lesser payback time and higher IRR which is also greater than the required rate of return of 15%.