Question

IRR, MIRR and Payback Period

The Follwoing 4 Questions depend on the CF of the following 2 projects and their WACC:

Project	CF0	CF1	CF2	CF3	CF4	WACC
A (3-year)	-100	40	50	60	N/A	.15
B (4-year	-73	30	30	30	30	.15

The IRR and MIRR of project A are: 7.7%, 16.3% 21.6%, 18.3% 23.3%, 18.6% 42.9%, 19.69%

A. 7.7%, 16.3%

B. 42.9%, 19.69%

C. 21.6%, 18.3%

D. 23.3%, 18.6%

The IRR and MIRR of project B are

A. 21.6%, 18.8%

B. 7.7%, 14.52%

C. 42.9%, 19.69%

D. 23.3%, 19.69%

The conventional and discounted payback periods for project A in years are:

A. 2.5, 3.6

B. 2.6, 3.4

C. 2.4, 3.5

D. 2.2, 3.7

The conventional and discounted payback periods for project B years are B:

A. none of these

B. 2.0, 3.8

C. 2.2, 4.1

D. 2.4, 4.3

D. 2.5, 3.7

Answer 1

1. IRR calculation:

-100 + 40/(1+r) + 50/(1+r)^2 + 60/(1+r)^3 =0

r= 21.648%

MIRR calculation formula:

MIRR=(FV(positive cashflows)/PV(negative cashflows))^1/n - 1

So, FV(positive cashflows) = 40x1.15^2 + 50x1.15 + 60 = 170.4

PV(negative cashflows) =100.

So, MIRR = (170.4/100)^1/3 - 1 = 18.3% Option C

2. IRR calculation:

-73 + 30/(1+r) +30/(1+r)^2 + 30/(1+r)^3 + 30/(1+r)^4=0

r=23.33%

For MIRR, we use the above formula.

FV(positive cashflows) = 30 x 1.15^3 + 30 x 1.15^2 + 30 x 1.15^1 + 30 = 149.8

PV(negative cashflows) = 73

MIRR = (149.8/73)^0.25 -1 = 19.68% Option D

3. The conventional payback will lie between years 2 and 3.

It will be = 2 + 10/60 = 2.16667

For Discounted payback, we calculate the present value of the amounts.

40/1.15 = 34.7826, 50/1.15^2=37.8, 60/1.15^2 = 45.368.

34.78 + 37.8 = 72.58. Remaining = 100-72.58 = 27.42. Therefore, the discounted payback = 2 + 27.42/45.368 = 2.6 years. The options given are wrong because the payback period can't run more than the life of the project.

4. Conventional Payback: Remaining amount after 2 years = 73-60 = 13

Conventioal Payback = 2 + 13/30 = 2.433 = 2.4 Option D