Re: 1998 Fall 5B #20

Richard Goldfarb ( (no email) )
Sat, 10 Apr 1999 14:41:01 -0700

This is another example of a poorly written question. It isn't entirely
clear what the CAS intended, but the 15% cost of capital APPEARS to be the
US $ discount rate because they specify that it is 2x the US risk free rate.
Since the risk free rate in punts is higher (9%), the risk adjusted rate in
punts will also be higher than the risk adjusted rate in dollars. To get
the punt risk adjusted rate, assume that the rate is the risk free rate of
9% plus the same relative risk premium. The book uses multiplicative risk
premiums for these types of questions, so in the us 1.15=1.075 * (1+risk
premium). Solve for the risk premium of 6.98% and apply that to the punt
risk free rate to get risk adjusted punt rate of 1.09*1.0698-1=16.6%.

Then the rest is just as you did. I get NPV of about 247. Answer D.

Note that you could've assumed that the risk premium was
additive, and therefore was 7.5% = 1.15-1.075 and then add that to the 9%
punt rate to get punt cost of capital of 16.5%. This is close to the 16.6%
found above, but in
this particular question if you rounded too much I think you would've had
the wrong answer. At 16.5% the NPV is 249.3. Still D, but answer E was
"$250 or more" so it would be close.

Be careful with these types of questions - I recommend sticking to
multiplicative risk premium since
that's the way the text did it.

Good luck.