CVP Analysis; Sustainability; Uncertainty; Decision Tables 

With gasoline prices increasing rapidly in recent years, consumers have moved to high miles-per-gallon (mpg) vehicles, in particular hybrid autos that rely on a battery as well as a gasoline engine for even greater mpg. The new vehicles save money on gas but also reduce the motorist’s “carbon footprint” in an environment of global warming. To encourage the purchase of fuel-efficient vehicles such as hybrids, the government may provide incentives, including income-tax credits, which represent dollar-for- dollar reductions in the income tax liability of the individual in the year of purchase. As both a cost-conscious and an environmentally conscious consumer, you are currently evaluating whether to purchase a hybrid vehicle. Assume that you have narrowed your decision down to two choices: a gasoline-powered vehicle or its equivalent hybrid (e.g., Ford Escape ver- sus Escape hybrid). Relevant information regarding each of these two vehicles is as follows:

Auto Cost Tax Credit Mpg

Gasoline model $17,000 n/a 23.0

Hybrid model $19,000 $500 27.0

Assume, further, that you plan to keep your auto for four years and that, based on recent experience, will likely drive the car 15,000 miles per year (60,000 miles in total).

Required

1. Generate a cost function for each decision alternative, where the dependent variable, Y, is “lifetime cost” and the independent variable, X, is “lifetime miles driven.”

2. Calculate the breakeven price for gas (per gallon) between the gasoline-powered model and the hybrid model. (Ignore the time value of money in your calculation.)

3. Prepare a graph for lifetime cost (Y) for each of the two autos as a function of price per gallon of gas (X), based on 60,000 lifetime miles for each auto. Use the following values of X (price per gal- lon of gas) to generate each cost function: $2.75, $3.00, $3.25, $3.50, $3.75, $4.00, $4.25, $4.50, $4.75, and $5.00. Properly label each graph, including the points of intersection. What can you conclude based on the graph you prepared?

4. This decision problem is similar to the choice-of-cost structure (variable vs. fixed) discussed in the chapter. Here, the issue is whether to pay an upfront premium (extra fixed cost) for the hybrid model, in exchange for lower variable costs over the life of the vehicle. In a typical CVP model, we were able, at any output level (X), to calculate a measure of profit sensitivity, which we called the degree of operating leverage (DOL). In the present context, which involves only costs for each vehicle over a four-year period, we cannot calculate DOL, but we might calculate an analogous measure: the ratio of % change in lifetime cost to % change in miles. Refer to this as a pseudo- DOL. Calculate this pseudo measure for each decision alternative, from a base of 60,000 lifetime miles. To calculate the percentage change figures, use 62,000 miles. What information is conveyed in the two measures you calculated?

5. The preceding calculations give you some of the information you need to make your decision. However, being the inquisitive type, you want more information. For example, you are wondering whether, in the present context (i.e., decision choice), the price of gas (per gallon) has much of an impact on the financial consequence regarding choice of automobile. To explore this issue further you decide to construct a decision table. As pointed out in the text, a decision table discloses com- binations of actions (here, choice of automobile), and events (here, lifetime miles driven, and mpg performance of each auto). Prepare a decision table that discloses the breakeven point in gas price for 50,000 miles, 60,000 miles, and 70,000 miles for each of five situations regarding the difference in initial cost (after rebate) between the gasoline-powered model and the hybrid model. Construct your table based on the following initial cost differences between the two: $2,500; $2,000; $1,500 (the base case, based on original data); $1,000; and, $500. (Hint: With five different initial cost dif- ferences and three alternatives for lifetime miles driven, your decision table should disclose 15 (i.e., 5 3 3) breakeven points in terms of price per gallon of gas.) Interpret a couple of points from the decision table you constructed.

6. The following probabilities (p) apply to the set of possible events (price of gas, per gallon) listed above in requirement 3: 0.05; 0.05; 0.05; 0.05; 0.15; 0.25; 0.15; 0.10; 0.10; and, 0.05. Your decision consists of one of two actions: buy the hybrid model, or buy the gasoline-powered model. Given this set of probabilities and events, calculate the expected value of the lifetime cost associated with each action (decision choice) under the assumption that lifetime miles driven 5 60,000. For each action, the expected value of lifetime cost, E(ai), is the weighted average of outcomes (lifetime costs), where the weights for each outcome are the outcome’s probability.

7. As noted in the preceding analyses, in some plausible scenarios the lifetime cost of each of the two decision alternatives is very close—in some cases they are practically indistinguishable. What non- financial (qualitative) factors and other quantitative factors (beyond those considered above) might be relevant to your decision? Explain.