Question

Chapter 12 Problem 3 (Excel functions needed)

Consider the project contained in Problem 7 in Chapter 11 (California Health Center).

a. Perform a sensitivity analysis to see how NPV is affected by changes in the number of procedures per day, average collection amount, and salvage value. Remember supplies vary with number of procedures.

b. Conduct a scenario analysis. Suppose that the hospital's staff concluded that the three most uncertain variables were number of procedures per day, average collection amount, and the equipment's salvage value. Furthermore, the following data were developed:

Scenario	Probabilty	Number of Procedures	Average Collection	Equipment Salvage Value
Worst	0.25	10	$60	$100,000
Most Likely	0.5	15	$80	$200,000
Best	0.25	20	$100	$300,000

c. Finally, assume that California Health Center's average project has a coefficient of variation of NPV in the range of 1.0 - 2.0. (Hint: Coefficient of variation is defined as the standard deviation of NPV divided by the expected NPV.) The hospital adjusts for risk by adding or subtracting 3 percentage points to its 10 percent corporate cost of capital. After adjusting for differential risk, is the project still profitable?

d. What type of risk was measured and accounted for in Parts b. and c.? Should this be of concern to the hospital's managers?

Answer 1

15.3 Consider the project contained in Problem 14.7 in Chapter 14.

a. Perform a sensitivity analysis to see how NPV is affected by changes in the number of procedures per day, average collection amount, and salvage value.

	Base NPV	NPV with change	%Change in NPV for variable
Rate of NPV's sensitivity to change in procedures per day	$50,871	$57,694.85	12%
Rate of NPV's sensitivity to change in collection period	$50,871	($112,764.93)	145%
Rate of NPV's sensitivity to change in salvage value	$50,871	$52,113.28	2%

b. Conduct a scenario analysis. Suppose that the hospital%u2019s staff concluded that the three most uncertain variables were number of procedures per day, average collection amount, and the equipment%u2019s salvage value. Furthermore, the following data were developed:

Number of Average Equipment

Scenario Probability Procedures Collection Salvage Value

Worst 0.25 10 $ 60 $100,000

Most likely 0.50 15 80 200,000

Best 0.25 20 100 300,000

Scenario	Probability	Procedures	Collection	salvage value
Worst	0.25	10	60	100,000
Most Likely	0.5	15	80	200,000
Best	0.25	20	100	300,000

Scenario	Probability	Procedures	Collection	salvage value
Worst	0.25	10	60	100,000
Most Likely	0.5	15	80	200,000
Best	0.25	20	100	300,000
	Expected value	15	80	200,000
	NPV for expected value of variable	$50,871.44	($261,525.26)	$50,871.44

c. Finally, assume that California Health Center%u2019s average project has a coefficient of variation of NPV in the range of 1.0%u20132.0. (Hint:

The coefficient of variation is defined as the standard deviation of NPV divided by the expected NPV.) The hospital adjusts for risk by adding or subtracting 3 percentage points to its 10 percent corporate cost of capital. After adjusting for differential risk, is the project still profitable?

Rate	NPV
+3% to cost of capital	$109,349.18
-3% to cost of capital	($373.08)

d. What type of risk was measured and accounted for in Parts b and c? Should this be of concern to the hospital%u2019s managers?

In part B, the essence was to measure how each variable would affect the expected NPV of the project. The risk is therefore the possibility that the variables would not be as expected.

On the other hand, the risk being evaluated in Part C is the interest rate risk. With this risk we measure the possibility that the NPV would become unfavorable for any change in interest rate.

From the computations, you will observe that under the scenario analysis, the expected values are highly sensitive to the collection period. As the collection period should therefore be of particular importance to management. On the other hand, the interest rate risk does not show any particularly unfavorable possibility of an unfavorable result.