Question

There are three projects listed below. The firm’s required rate of return is 13%. Please show work.

Year	Project AB	Project LM	Project UV
0	$ (90,000)	$ (100,000)	$ (96,500)
1	39,000	0	(55,000)
2	39,000	0	100,000
3	39,000	147,500	100,000

a) Compute net present value and internal rate of return of each project

Project	AB	LM	UV
NPV
IRR

b) If three projects are mutually exclusive, which one should be chosen?

c) What is the discount rate when NPV_AB equals NPV_UV (i.e., crossover rate)?

ΔCF0=                        ΔCF1=                                      ΔCF2=                                 ΔCF3=     

IRR=

d) Compute the traditional payback period for each project.

e) Please follow the steps below to compute modified IRR (MIRR) of Project UV.

1) PV of cash outflows:

2) FV of cash inflows:

3) MIRR:

Answer 1

NPV is given by:

Answer a)

Project AB

NPV = [ 39000 / (1 + 13%)^¹ ] + [ 39000 / (1 + 13%)^² ] + [ 39000 / (1 + 13%)^³ ] - Initial Investment

NPV = 34513.27 + 30542.72 + 27028.96 - 90000

NPV = $2084.95

Also

for IRR = r

NPV = 0 = [ 39000 / (1 + r%)^¹ ] + [ 39000 / (1 + r%)^² ] + [ 39000 / (1 + r%)^³ ] - Initial Investment

[ 39000 / (1 + r%)^¹ ] + [ 39000 / (1 + r%)^² ] + [ 39000 / (1 + r%)^³ ] - 90000 = 0

Hence,

r = 14.36%

Project LM

NPV =  [ 147500 / (1 + 13%)^³ ] - Initial Investment

NPV = 102224.90 - 100000

NPV = $ 2224.90

Also

for IRR = r

NPV = 0 = [ 147500 / (1 + r%)^³ ]- Initial Investment

[ 147500 / (1 + r%)^³ ] - 100000 = 0

Hence,

r = 13.83%

Project UV

NPV = [ -55000 / (1 + 13%)^¹ ] + [ 100000 / (1 + 13%)^² ] + [ 100000 / (1 + 13%)^³ ] - Initial Investment

NPV = -48672.57 + 78314.67 + 69305.02 - 96500

NPV = $2447.12

Also

for IRR = r

NPV = 0 = [ -55000 / (1 + r%)^¹ ] + [ 100000 / (1 + r%)^² ] + [ 100000 / (1 + r%)^³ ] - Initial Investment

[ -55000 / (1 + r%)^¹ ] + [ 100000 / (1 + r%)^² ] + [ 100000 / (1 + r%)^³ ] - 96500 = 0

Hence,

r = 13.89%

Project	AB	LM	UV
NPV	2084.95	2224.9	2447.12
IRR	14.36%	13.83%	13.89%

---------------------------------------------

Answer b)

If mutually exclusive, choose Project UV

because,

NPV is highest for Project UV and also IRR > WACC and highest

-----------------------------------

Answer c)

Step 1: Find difference in cashflows

Step 2: FInd IRR

Year	AB	UV		AB-UV
0	-$90,000	-$96,500		6500 (-90000 - (-96500))
1	$39,000	-$55,000		94000 (39000 - (- 55000))
2	$39,000	$1,00,000		-61000
3	$39,000	$1,00,000		-61000

Hence now find IRR

for IRR = r

NPV = 0 = [ 94000 / (1 + r%)^¹ ] + [ -61000 / (1 + r%)^² ] + [ -61000 / (1 + r%)^³ ] - Initial Investment

Hence,

r = 13.30% [Cross Over Rate]

-------------------------------------

Answer d)

Find cumulative cashflows

Project AB
Initial Investment		90,000
year	Cashflow	Cumulative Cashflow
1	39,000	39,000
2	39,000	78,000 (39000 + 39000)
3	39,000	1,17,000 (78000 + 39000)

In year 2, we got back $ 78000 of the invested amount $ 90000

Remaining (98000 - 78000) = $ 12000 needs to be earned in year 3

In year 3 we are earning 39000

Hence to earn $ 12000, time required = 12000 / 39000 = 0.31

Hence, payback period = Year 2 + 0.31 (Year 3) = 2.31 Years

Project LM
Initial Investment		1,00,000
year	Cashflow	Cumulative Cashflow
1	-
2	-
3	1,47,500	1,47,500

In year 3 we are earning 147500

Hence to earn $ 100000, time required = 100000 / 147500 = 0.68

Hence, payback period = Year 2 + 0.68 (Year 3) = 2.68 Years

Project UV
Initial Investment		96,500
year	Cashflow	Cumulative Cashflow
1	-55,000	-55,000
2	1,00,000	45,000 (-55000 + 100000)
3	1,00,000	1,45,000 (45000 + 100000)

In year 2, we got back $ 45000 of the invested amount $ 96500

Remaining (96500 - 45000) = $ 51500 needs to be earned in year 3

In year 3 we are earning 100000

Hence to earn $ 51500, time required = 51500 / 100000 = 0.52

Hence, payback period = Year 2 + 0.52 (Year 3) = 2.52 Years