Question

The Yoran Yacht Company (YYC), a prominent sailboat builder in Newport, may design a new 30-foot sailboat based on the "winged" keels first introduced on the 12-meter yachts that raced for the America's Cup.

First, YYC would have to invest $14,000 at t = 0 for the design and model tank testing of the new boat. YYC's managers believe there is a 60% probability that this phase will be successful and the project will continue. If Stage 1 is not successful, the project will be abandoned with zero salvage value.

The next stage, if undertaken, would consist of making the molds and producing two prototype boats. This would cost $500,000 at t = 1. If the boats test well, YYC would go into production. If they do not, the molds and prototypes could be sold for $100,000. The managers estimate that the probability is 80% that the boats will pass testing and that Stage 3 will be undertaken.

Stage 3 consists of converting an unused production line to produce the new design. This would cost $1 million at t = 2. If the economy is strong at this point, the net value of sales would be $3 million; if the economy is weak, the net value would be $1.5 million. Both net values occur at t = 3, and each state of the economy has a probability of 0.5. YYC's corporate cost of capital is 11%.

1. Assume this project has average risk. Construct a decision tree and determine the project's expected NPV. Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

2. Find the project's standard deviation of NPV and coefficient of variation (CV) of NPV. Do not round intermediate calculations. Round the project's standard deviation to the nearest cent and CV to two decimal places.

   σ_NPV: $  

   CV_NPV:

   If YYC's average project had a CV of between 1.0 and 2.0, would this project be of high, low, or average stand-alone risk?

   This project is of

1. risk.

Answer 1

Decision tree:

a). Expected NPV = 125,577.12

b). Project Standard deviation (SD) = 460,093.95

Coefficient of variation (CV) = SD/Expected NPV = 460,093.95/125,577.12 = 3.66

If average project has a CV between 1.0 and 2.0 then this project is high risk.

Calculations:

For calculating the NPV, first NPV along each branch is calculated along with the joint probability of that branch.

For example, for the branch: strong economy, NPV = -14,000 - 500,000/(1+11%) - 1,000,000/(1+11%)^2 + 3,000,000/(1+11%)^3 = 917,501.26

Joint probabililty along the branch: strong economy will be the multiplication of all probabilities along that branch so it is 60%*80%*50% = 24.00%

Expected NPV of the project = sum of (NPV*Joint Probability)

Full image with decision tree:

Time (n) T=0 T=1 T= 2 T=3 Strong economy P = 50% 3000000 Successful testing Prototype production P = 60% -500000 Prototypes successful Production starts P = 80% -1000000 Weak economy P = 50% 1500000 Prototypes unsuccessful P=20% 100000 -14000 Unsuccessful testing P = 40% 0

Time (n) T = 0 T = 1 T = 2 Decision tree branch NPV Joint Probability NPV JP JP (NPV-Expected NPV)^2 T=3 Strong economy P = 50% 3000000 Strong economy 917501.26 24.00% Prototypes successful Production starts P = 80% - 1000000 220200.30 150514521467.31 Successful testing Prototype production P = 60% -500000 Weak economy P = 50% 1500000 Weak economy -179285.81 24.00% -43028.59 22305938122.54 Prototypes unsuccessful P = 20% 100000 - 14000 Prototype unsuccessful -383288.21 12.00% -45994.58 31073270877.22 Unsuccessful testing P = 40% 0 40.00% -5600.00 7792709281.03 Unsuccessful testing - 14000.00 Formulas: Sum of (NPV*JP) Sum of JP (NPV-Expected NPV)^2 Variance^0.5 Standard deviation/Expected NPV Expected NPV Variance Standard deviation CV 125577.12 211686439748.10 460093.95 3.66