Answers to End–of–Chapter Problems
9-1
Chapter 9 :Risk Analysis, Real Options, and Capital Budgeting
9.1
a
.
To calculate the accounting breakeven, we first need to find the depreciation for each year. The
depreciation is:
Depreciation = $724,000 / 8
Depreciation = $90,500 per year
And the accounting breakeven is:
Q
A
= ($850,000 + $90,500) / ($39 – $23)
Q
A
= 58,781 units
b.
We will use the tax shield approach to calculate the Operating Cash Flow, OCF. The OCF is:
OCF
base
= [(Price – Variable cost)
×
Sales units – Fixed cost]
×
(1 – T
c
) + T
c
×
Depreciation
OCF
base
= [($39 – $23)
×
75,000 – $850,000]
×
(0.65) + 0.35
×
($90,500)
OCF
base
= $259,175
Now we can calculate the NPV using our base-case projections. There is no salvage value or NWC, so
the NPV is:
NPV
base
= –$724,000 + $259,175
×
8
%
15
Α
NPV
base
= $439,001.55
To calculate the sensitivity of the NPV to changes in the quantity sold, we will calculate the NPV at a
different quantity. We will use sales of 80,000 units. The NPV at this sales level is:
OCF
new
= [($39 – $23)
×
(80,000) – $850,000]
×
(0.65) + 0.35
×
($90,500)
OCF
new
= $311,175
And the NPV is:
NPV
new
= – $724,000 + $311,175
×
8
%
15
Α
NPV
new
= $672,342.27
So, the change in NPV for every unit change in sales is:
Δ
NPV/
Δ
S = ($439,001.55 – $672,342.27) / (75,000 – 80,000)
Δ
NPV/
Δ
S = $46.668
If sales were to drop by 500 units, then NPV would drop by:
NPV drop = $46.668
×
(500) = $23,334.07
You may wonder why we chose 80,000 units. It doesn’t matter! Whatever sales number we use, when
we calculate the change in NPV per unit sold, the ratio will be the same.