Homework 4 2018 solution.doc

# 1 between the standard without upgrade package and

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(1) Between the standard (without upgrade package) and premium machines, do a breakeven analysis with respect to X. (2) Assume the premium machine is not available now, and the company can only buy the standard one. What is the highest price of the upgrade package, as a function of X, so that the company is willing to buy the package? (3) Assume X=100%. What is the highest price of the upgrade package so that the company is willing to buy it? [Note: these three questions are independent]. General remarks: In the solution given below, we assume that by the end of Year 2, we would know whether there is a demand increase; then we can decide whether to swap to the premium machine (given the upgrade package already bought), and the extra 20000 will be paid at the beginning of Year 2. Alternative assumptions are acceptable. (1) Standard machine, PW1= 24000(P/A,3%,5) – 100000 Premium machine, with 1-X probability, PW2= 24000(P/A,3%,5) – 120000 with X probability, PW3= 24000(P/A,3%,5) + 10000(P/A,3%,3)(P/F,3%,2) – 120000 At breakeven, we have PW1 = (1 – X)PW2 + XPW3. Hence X=75% If X is much higher than 75%, we choose the premium machine; if X is much lower than 75%, we choose the standard machine. If X is around 75%, choosing either one would be fine.

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(2) Let the price be Y.
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• Fall '14
• Year Three, Year Two, 1-X probability

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