Question

Consider the following project’s cash flows:

Year    End-of-year Cash Flow

0. –$1,000
1. -$2,000
2. $2,000
3. $1,500

A. What is this project’s net present value if the discount rate is 6 percent?

B. What is this project’s internal rate of return?

C. What is this project’s modified internal rate of return if the reinvestment rate is 5 percent?

D. What is this project’s modified internal rate of return if the reinvestment rate is 6 percent?

Answer 1

A)

NPV = Sum of PV all cash flow

PV=CF/(1+r)^n

where CF= cash flow

r=6%

n=year in which cash flow occur

Foe n=1

PV=2000/(1+6%)^1=$1886.79

Year	Cash flow	PV of Cash flow
0	-1000	-1000.00
1	2000	1886.79
2	2000	1779.99
3	1500	1259.43
NPV		3926.21

B)

At internal rate of return ,NPV =0

Let r be internal rate of return

So NPV=0

-1000/(1+r)^0+2000/(1+r)^1+ 2000/(1+r)^2+ 1500/(1+r)^3 =0

Solving for r we get

r=187.66%

C)

Here n=3 years

reinvestment rate =5%

FV of Positive cash flow =2000*(1+5%)^2+2000*(1+5%)^1+1500*(1+5%)^0=$5805

PV of Cash outflow=-$1000

MIRR=(5805/-(-1000))^(1/3)-1=79.72%

D)

reinvestment rate =6%

FV of Positive cash flow =2000*(1+6%)^2+2000*(1+6%)^1+1500*(1+6%)^0=$5867.2

PV of Cash outflow=-$1000

MIRR=(5867.2/-(-1000))^(1/3)-1=80.36%