Problem Set II Solutions
Capital Budgeting and Risk Return
Problem 1
Discount rate = 10%
A)
NPV of investing in machine A can be calculated as sum of present value of the cash
flows (cash outflow at t = 0 and annuity for next six years).
NPV (Machine A) = -$1,000,000 +
$gG±,±±±
±.²
³1 −
²
².²
´
µ
= $88,815.17
NPV of investing in machine B can be calculated as sum of present value of the cash
flows (cash outflow at t = 0 and annuity for next three years; and cash flow at t = 3 and
another annuity for next three years).
NPV (Machine B) =
¶−$400,000 +
$g±±,±±±
±.²
³1 −
²
².²
·
µ¸
+
²
².²
·
¶−$400,000 +
$g±±,±±±
±.²
³1 −
²
².²
·
µ¸
= $170,526.22
As NPV of machine B is greater than NPV of machine A, company should buy machine B.
B)
NPV of machine A in this case remains same.
NPV (Machine B) =
¶−$400,000 +
$g±±,±±±
±.²
³1 −
²
².²
·
µ¸
+
²
².²
·
¶−$550,000 +
$g±±,±±±
±.²
³1 −
²
².²
·
µ¸
= $57,829
As in this case, NPV of machine A is greater than NPV of machine B, company should buy
machine A.
Problem 2
a)
Even though the firm will only know if they get the contract a year from now, they have
to commit to buy the equipment today. The chance of getting the contract is 70%.
Hence the chance of future inflows is also 70%.The inflows start at year 2 for a period of
10 years.
Years
0
1
2
3
e
10
11
|―――――――|――― ―――|―――――――|――― ―――|――― ―――|――― ―――|
Investment
-$1,000,000
Contract awarded (p=70%)
$ 250,000
$ 250,000
e
$ 250,000
$ 250,000
Contract lost (p=30%)
$ 0
$ 0
e
$ 0
$ 0
Int rate (yearly)
|―
―|
Present values
Investment
PV
annuity won
PV
annuity lost
15%