Use the following information for the next three problems, PV of Year Cash Flow
ID: 2765759 • Letter: U
Question
Use the following information for the next three problems,
PV of
Year
Cash Flow
Cash Flows
1
$14,000
$12,726
2
$14,000
$11,564
3
$10,000
$7,510
4
$10,000
$6,830
5
$8,000
$4,968
6. What is the NPV of above project if the initial investment was $35,000?
7. Calculate the IRR assuming a cost of capital of 11%.
8. Calculate the MIRR of the project assuming a cost of capital of 11%.
PV of
Year
Cash Flow
Cash Flows
1
$14,000
$12,726
2
$14,000
$11,564
3
$10,000
$7,510
4
$10,000
$6,830
5
$8,000
$4,968
Explanation / Answer
(6)
Sum of PV of cash inflows = $(12,726 + 11,564 + 7,510 + 6,830 + 4,968) = $43,598
NPV = Sum of PV of cash inflows - initial investment = $(43,598 - 35,000) = $8,598
(7) To compute IRR, cost of capital is not required.
IRR is that discount rate which makes NPV equal to zero and is found using approximation method as:
IRR = RL + [NPVL / (NPVL - NPVH)] x (RH - RL) where
RH: Higher interest rate = 12% (assumed),
RL: Lower interest rate = 6% (assumed)
NPVH: NPV at higher rate
NPVL: NPV at lower rate
So, IRR = 6% + [12,963 / (12,963 - 6,673)] x (12 - 6)%
= 6% + [12,963 / 6,290] x 6%
= 6% + 2.06 x 6%
= 6% + 12.36%
= 18.36%
NOTE: First 2 questions are answered.
Year Cash Flow Discount factor@6% Discounted Net Benefit Discount factor@12% Discounted Net Benefit (A) (B) (A) x (B) (C) (A) x (C) 0 -35,000 1.0000 -35,000 1.0000 -35,000 1 14,000 0.9434 13,208 0.8929 12,500 2 14,000 0.8900 12,460 0.7972 11,161 3 10,000 0.8396 8,396 0.7118 7,118 4 10,000 0.7921 7,921 0.6355 6,355 5 8,000 0.7473 5,978 0.5674 4,539 NPV = 12,963 NPV = 6,673