The case

The financial pathway to green manifests itself as a dichotomous and mutually-exclusive choice between a hybrid car which entails fossil fuel directly and an all-electric car which doesn’t. This exercise frames the decision-making process into a typical mutually-exclusive capital budgeting analysis. We choose Toyota Prius as the hybrid and the Nissan Leaf as the all-electric car.

In August 2015, a Toyota Prius lists at $26,985 as its manufacturer suggested retail price. The corresponding retail price for the Nissan Leaf lists at $29,010.

The Prius has a city-highway combined efficiency of 50 miles per gallon. For the base-case analysis, let’s assume a gas price at $3.00 per gallon. This will result in a mileage efficiency of 6 ¢/mile.

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The Leaf has an efficiency of 5.4 miles/kWh. For base-case analysis, let’s assume electricity supply at a price of 12 ¢/kWh. This will result in a mileage efficiency of 2.2222 ¢/mile.

For simplicity of analysis, let’s assume the a driver who needs to drive 12,000 miles a year or 1,000 miles a month for work, school, and other transportation needs. Let’s further assume the driver faces an auto loan’s interest rate of 3% per year or .25% per month.

To do: We first perform a base-case analysis using the data provided or assumed so far.

Q1: Calculate the monthly cash flows for purchasing and operating the Prius for 10 years. (10%)

Q2: Calculate the monthly cash flows for purchasing and operating the Leaf for 10 years. (10%)

Q3: From the monthly cash flows in the previous two questions, derive the incremental cash flows of purchasing the more expensive Leaf over the less-expensive Prius for 10 years. (10%)

Q4: From the incremental cash flows established in Q3 above, find the following capital-budgeting measures.

i. undiscounted payback in years; (5%)

ii. discounted payback in years; (5%)

iii. net present value, NPV, in $; (10%)

iv. internal rate of return, IRR, in % (10%)

v. profitability index (practitioner’s version) (10%)

vi. modified internal rate of return, MIRR, in %. Use reinvestment rate of 1% per annum or .08333% per month. (10%)

Next, we perform 2-variable sensitivity analyses over ranges of plausible values for the two variables by calculating the discount payback which is simply the number of years it entails to breakeven the extra $2,025 upfront payment for the all-electric Nissan Leaf. For the Prius, we choose gas price as the variable for a range of 2.00 $/gallon to 6.00 $/gallon over a 50-¢ increment. For the Leaf, we choose three variables, namely the interest rate from 0% to 6% per year, electric supply rate from 8 ¢/kWh to 16 ¢/kWh, and tax credit for buying the electric car from $0 (the base-case analysis above) to $2,000 at $500 increment. Beware of the #NUM! output when applying the Excel’s Data, What-if Analysis, Data Table mode. They are not spurious output but do have their own significant economic interpretation. Those who need help with the Data Table function in Excel, please refer to the Appendix where a similar numerical example was presented as an illustration.

We expect three output tables as follow:

Gas price, $/gallon

2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00

Interest rate, % p.a. 0

1

2

3

4

5

6

Table 1: Discounted payback, in years, of an all-electric Leaf over the hybrid Prius at various gas prices and various auto loan interest rates. (20%)

Gas price, $/gallon

2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00

Electricity rate, ¢/kWh 8

9

10

11

12

13

14

15

16

Table 2: Discounted payback, in years, of an all-electric Leaf over the hybrid Prius at various gas prices and various electricity supply charge rates. (20%)

Gas price, $/gallon

2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00

Tax credit for electric car, $ 0

500

1500

2000

2025

Table 3: Discounted payback, in years of an all-electric Leaf over the hybrid Prius at various gas prices and various tax credit levels. (20%)

Q5: What does the output #NUM! mean financially in Table 1 if you change the price spread from $2,025 to $4,000? Use numbers to justify your answer.

Now, change the price spread back to $2,025 before answer the following questions.

Q6: From Table 1, make two ceteris paribus statements on the discounted payback on each variable. Then, make another combined statement on discounted payback’s trend based on both variables. (20%)

Q7: From Table 2, make two ceteris paribus statements on the discounted payback on each variable. Then, make another combined statement on discounted payback’s trend based on both variables.

(20%)

Q8: From Table 3, make two ceteris paribus statements on the discounted payback on each variable. Then, make another combined statement on discounted payback’s trend based on both variables.

(20%)

Appendix

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