Biomedical Engineering Reference
In-Depth Information
Self-Test 11.3
a. Undiscounted, the value of the streams simple $170,000 in costs and
$180,000 in benefits, so it is a good investment.
Year 1
Year 2
Year 3
Year 4
Year 5
Present value
Costs
$100,000
$40,000
$10,000
$10,000
$10,000
$170,000
Benefits
0
$30,000
$40,000
$50,000
$60,000
$180,000
b. The undiscounted cost-benefit ratio is $170,000/$180,000 or 0.94, indi-
cating that it costs you 94 cents for each dollar of return.
c. To calculate the present value of a discounted stream, each year's costs
and benefits must be discounted by
X
r
PV
=
t
(
)
1
+
which produces the following table (for the first entry, 0.9524
¥
100,000
=
$95,239, excluding rounding error.
Year 1
Year 2
Year 3
Year 4
Year 5
Present value
Discount multiplier
0.9524
0.9070
0.8638
0.8227
0.7835
Costs
$95,238
$36,281
$8,638
$8,227
$7,835
$156,220
Benefits
$0
$27,211
$34,554
$41,135
$47,012
$149,911
d. The cost-benefit ratio is now $156,220/$149,911, or 1.04, indicating an
unfavorable CB ratio.
This example shows that, when the majority of costs occur early and bene-
fits occur late in a project, discounting can change the conclusion about cost
benefit.
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