52
Berk/DeMarzo
•
Corporate Finance
So the value today is
()
royalties
3
12.5
PV
9.391
1.1
==
Now add this to the NPV from part a), NPV
9.895
9.391
$503,381
=−
+
.
6-3.
a.
Timeline:
0
1
2
3
6
7
16
-200,000 -200,000 -200,000
-200,000 300,000
300,000
i.
66
1
0
1
0
200,000
1
1
300,000
1
NPV=-
1-
+
1-
rr
1+r
1+r
1+r
200,000
1
1
300,000
1
=-
1-
+
1-
0.1
0.1
1.1
1.1
1.1
=$169,482
⎛⎞
⎛
⎞
⎛
⎞
⎜⎟
⎜
⎟
⎜
⎟
⎝⎠
⎝
⎠
⎝
⎠
⎛
⎞
⎛
⎞
⎜
⎟
⎜
⎟
⎝
⎠
⎝
⎠
NPV>0, so the company should take the project.
ii.
Setting the NPV = 0 and solving for r (using a spreadsheet) the answer is IRR = 12.66%.
So if the estimate is too low by 2.66%, the decision will change from accept to reject.
iii.
The new timeline is
0
1
2
3
N
N+1
N+10
-200,000 -200,000 -200,000
-200,000 300,000
300,000
NN
1
0
200,000
1
1
300,000
1
NPV=-
1-
+
1-
1+r
1+r
1+r
⎛
⎞
⎜
⎟
⎝
⎠
Setting the NPV = 0 and solving for N gives
10
10
300,000
500,000-
1+r
log
200,000
1.5
log 2.5-
1.1
N=
=
=6.85 years
log 1+r
log 1.1
⎝
⎠