Question

In: Finance

Project Cash Flow Today (millions) Cash Flow in One Year (millions) A -$10 $20 B $6...

Project	Cash Flow Today (millions)	Cash Flow in One Year (millions)
A	-$10	$20
B	$6	$4
C	$18	-$12

Suppose all cash flows are certain and the risk-free interest rate is 5%.

a. What is the NPV of each project?

b. If the firm can choose only one of these projects, which should it choose?

c. If the firm can choose any two of these projects, which should it choose?

Expert Solution

a.

PV factor for year 1, F1 = 1/ (1+r) ⁿ

r is rate of interest( 5 %) and no. of year, n is 1

F1 = 1/ (1+5%) = 1/(1+0.05) = 1/1.05 = 0.952380952

NPV of Project A = PV of cash flow in year one - PV of cash flow today

= $ 20,000,000 x F1 - $ 10,000,000

= $ 20,000,000 x 0.952380952 - $ 10,000,000

= $ 19,047,619.05 - $ 10,000,000 = $ 9,047,619.05

NPV of Project B = PV of cash flow in year one + PV of cash flow today

= $ 4,000,000 x F1 + $ 6,000,000

= $ 4,000,000 x 0.952380952 + $ 6,000,000

= $ 3,809,523.81 + $ 6,000,000 = $ 9,809,524

NPV of Project C = PV of cash flow in year one + PV of cash flow today

= - $ 12,000,000 x F1 + $ 18,000,000

= -$ 12,000,000 x 0.952380952 + $ 18,000,000

= $ 18,000,000 - $ 11,428,571.43 = $ 6,571,428.57

[In Project B both cash flows are positive where as in Project C cash flow in year 1 is negative]

b.

The firm can choose Project B, as its NPV is highest.

c.

The firm can choose Project B and Project A as their NPVs are higher than Project C.

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