Question

Multiple Rates of Return

The Ulmer Uranium Company is deciding whether or not to open a strip mine whose net cost is $4.4 million. Net cash inflows are expected to be $27.7 million, all coming at the end of Year 1. The land must be returned to its natural state at a cost of $25 million, payable at the end of Year 2.

What is the project's MIRR at r = 8%? Do not round intermediate calculations. Round your answer to two decimal places.
7.61 % (Correct Answer)

What is the project's MIRR at r = 14%? Do not round intermediate calculations. Round your answer to two decimal places.
%

Calculate the two NPVs. Do not round intermediate calculations. Round your answers to the nearest cent.

1    $  

2    $  

Answer 1

The modified internal rate of return (MIRR) assumes that positive cash flows are reinvested at the firm's cost of capital, and that the initial outflows are financed at the firm's financing cost.

The MIRR can be calculated with the below steps .

Year 0		Year 1		Year 2
$4.4M Outflow		$27.7 Inflow		$25M Outflow

Step 1) We calculate the PV of the outflows at 8%

PV of the outflows = 4.4 + 25 / ( 1 + 0.08) ^2

= 4.4 + 25 / 1.1664

= 4.4 + 21.43

= 25.83

Step 2) We calculate the Future value of inflows @ 8%

FV of inflows = 27.7 * (1 + .08)

= 29.92

Step 3) Equate the PV of the outflows with the PV of FV of inflows and solve for x.

PV of outflows = PV of ( FV of Inflows)

25.83 = 29.92 / ( 1+ x) ^2

25.83 * (1 + x) ^2 = 29.92

( 1+ x) ^2 = 29.92 / 25.83

(1 + x) =(1.1583) ^0.5

1+ x = 1.0761

x = 7.61%

MIRR = 7.61%

Step 1) We calculate the PV of the outflows at 14%

PV of the outflows = 4.4 + 25 / ( 1 + 0.14) ^2

= 4.4 + 25 / 1.2996

= 4.4 + 19.24

= 23.64

Step 2) We calculate the Future value of inflows @14%

FV of inflows = 27.7 * (1 + .14)

= 31.58

Step 3) Equate the PV of the outflows with the PV of FV of inflows and solve for x.

PV of outflows = PV of ( FV of Inflows)

23.64 = 31.58 / ( 1+ x) ^2

23.64 * (1 + x) ^2 = 31.58

( 1+ x) ^2 = 31.58 / 23.64

(1 + x) =(1.3359)^0.5

1+ x = 1.1558

x= 15.58 %

MIRR = 15.58%

NPV @ 8% = Pv of inflows - Pv of outflows

= 27.7 / 1.08 - { 4.4 + 25 / (1.08) ^2}

= 25.65 - ( 4.4 + 25/1.1664)

= 25.65 - ( 4.4 + 21.43 )

= 25.65 - 25.83

=-$0.18 M

NPV @ 14% = 27.7 / 1.14 - { 4.4 + 25 /1.14^2}

=24.30 - ( 4.4 + 25/1.2996)

= 24.30 - ( 4.4 + 19.24)

= 24.30 - 23.64

= $0.66 M