Question

P12-4 (similar to) Basic scenario analysis   Prime Paints is in the process of evaluating two mutually exclusive additions to its processing capacity. The​ firm's financial analysts have developed​ pessimistic, most​ likely, and optimistic estimates of the annual cash inflows associated with each project. These estimates are shown in the following table. Project A Project B Initial investment 12,500 12,500 ​(CF 0CF0​) Outcome Annual cash inflows ​(CF CF ​) Pessimistic ​$880 ​$1,550 Most likely 1,690 1,690 Optimistic 2,420 1,790 a. Determine the range of annual cash inflows for each of the two projects. b. Assume that the​ firm's cost of capital is 10.5 %10.5% and that both projects have 17​-year lives. Construct a table showing the NPVs for each project for each of the possible outcomes. Include the range of NPVs for each project. c. Do parts ​(a​) and ​(b​) provide consistent views of the two​ projects? Explain. d. Which project do you​ recommend? Why? a. The range of annual cash inflows for project A is ​$nothing.

Answer 1

A) Determine the range of annual cash inflows for each of the two projects

Range A = $2420 - $880 = $1540

Range B = $1790 - $1550 = $240

B) Assume that the​ firm's cost of capital is 10.5% and that both projects have 17​-year lives. Construct a table showing the NPVs for each project for each of the possible outcomes. Include the range of NPVs for each project

Calculation of NPV for different outcomes for Project A:

Pessimistic:

Rate = 10.5%

Nper = 17 years

PMT = -880

Using excel,

=pv(10.5%,17,-880,0)

= $6845.86

Cash outflow = -12500

NPV = -12500 + 6845.86

NPV = -$5654.14

Most Likely:

Rate = 10.5%

Nper = 17 years

PMT = -1690

Using excel,

=pv(10.5%,17,-1690,0)

= $13147.16

Cash outflow = -12500

NPV = -12500 + 13147.16

NPV = $647.16

Optimistic:

Rate = 10.5%

Nper = 17 years

PMT = -2420

Using excel,

=pv(10.5%,17,-2420,0)

= $18826.11

Cash outflow = -12500

NPV = -12500 + 18826.11

NPV = $6326.11

Calculation of NPV for different outcomes for Project B:

Pessimistic:

Rate = 10.5%

Nper = 17 years

PMT = -1550

Using excel,

=pv(10.5%,17,-1550,0)

= $12058.05

Cash outflow = -12500

NPV = -12500 + 12058.58

NPV = -$441.95

Most Likely:

Rate = 10.5%

Nper = 17 years

PMT = -1690

Using excel,

=pv(10.5%,17,-1690,0)

= $13147.16

Cash outflow = -12500

NPV = -12500 + 13147.16

NPV = $647.16

Optimistic:

Rate = 10.5%

Nper = 17 years

PMT = -1790

Using excel,

=pv(10.5%,17,-1790,0)

= $13925.10

Cash outflow = -12500

NPV = -12500 + 13925.11

NPV = $1425.10

NPVs of project A and Project B under different outcomes:

	NPVs
Outcome	Project A	Project B
Pessimistic	($5,654.14)	($441.95)
Most likely	647.16	647.16
Optimistic	6,326.11	1,425.10
Range =	11,980	1,867

C) Do parts ​(a​) and ​(b​) provide consistent views of the two​ projects? Explain.

Since the initial investment of projects A and B are equal, the range of cash flows and the range of NPVs are consistent

D) Which project do you​ recommend?

Project selection would depend upon the risk disposition of the management. (A is more risky than B but also has the possibility of a greater return.)