Question

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.

The Leaf has an efficiency of 5.4 miles/kWh.[1] 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.[2]

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%)

[1]   We obtain the 5.4 miles per kWh statistic from http://insideevs.com/long-term-nissan-leaf-mileageusage-review-once-around-the-sun/.

[2] The 2.2222 cents per mile number is consistent with Sharon Terlep’s article in The Wall Street Journal, August 12, 2009, where she reported the Chevrolet Volt’s lithium-ion battery pack can deliver a range of 40 miles before it needs recharging at 88 cents per charge. The Leaf has a range of 84 miles per full charge. We did not choose the Volt because the Volt is not an all-electric car with its fossil-fuel internal combustion engine backup propulsion.

Answer 1

1 & 2.  

Monthly cash flow for both Prior and Leaf as below

Please see that interest charge on purchase of car = 0.25% x Price of car. (Could have used the amortization cost, but since Interest is mentioned as 0.25% per month)

	Toyota Prius	Nissan Leaf
Cost of Car ($) A	$26,985	$29,010
Loan period years	10	10
Fuel/ Energy cost per mile (Cents) B	6	2.2222
Fuel/ Energy cost per month driving 1000 miles($) C = B x 1000	$60.00	$22.22
Loan Monthly Interest cost at 0.25% per month D = A x 0.25%	$67.46	$72.53
Monthly Cash flow E = C + D	$127.46	$94.75
Yearly cashflow F = 12 X E	$1,529.55	$1,136.96

3. & 4.

Using the above and then Converting in annual cash flows

The incremental cost = 26,985 -29,010 = - $2025

The incremental cashflow for all years ( It is same for all years) = 1529.55 - 1136.96 = $392.59

The table looks like

Year	Incremental Cash flow	PV of Cash Flows (Discounted at 3%)	Cumulative Cash Flows for Pay back period	Discounted Cumulative Cash Flows (PV) for Disc Pay Back period	Future Value of Cash Flows using 1% reinvestment rate
0	($2,025.00)	($2,025.00)	($2,025.00)	($2,025.00)	($2,025.00)
1	$392.59	$381.15	($1,632.41)	($1,643.85)	$429.37
2	$392.59	$370.05	($1,239.83)	($1,273.80)	$425.11
3	$392.59	$359.27	($847.24)	($914.53)	$420.91
4	$392.59	$348.81	($454.66)	($565.72)	$416.74
5	$392.59	$338.65	($62.07)	($227.07)	$412.61
6	$392.59	$328.78	$330.52	$101.71	$408.53
7	$392.59	$319.21	$723.10	$420.92	$404.48
8	$392.59	$309.91	$1,115.69	$730.83	$400.48
9	$392.59	$300.88	$1,508.27	$1,031.72	$396.51
10	$392.59	$292.12	$1,900.86	$1,323.84	$392.59
PayBack Period			5.16
Discounted Pay Back Period				5.69
IRR	14.29%
NPV		$1,323.84
MIRR					7.328%
Profitability Index		1.65

a. IRR is calculated using excel function for IRR with incremental values of Price and cash flows = 14.29%

b. Pay Back Period is calculated using the cumulative cash flows

The Cumulative cash flows turn positive in year 6. The pay back is between 5 & 6 years

Pay Back period = 5 + Cumulative cash flow in year 5 (the negative value)/ CF in year 6

= 5 + 62.07/392.59 = 5.16

c. Discounted pay back period is calculated using discounted cash flows (at 3%)

The Cumulative cash flows turn positive in year 6. The pay back is between 5 & 6 years

Pay Back period = 5 + Cumulative discounted cash flow in year 5 (the negative value)/ Discounted CF in year 6

= 5 + 227.07/328.78 = 5. 69

D. NPV is calculated using a discount rate of 3%

PV = CFt / (1+k)^t

where CFt = Cash flow in year t

K = Discount rate

t is the year of discount

For example PV of 7th year = 392.59 / (1+3%)^7 = $319.21

Thus NPV = Sum of all PVs - Initial cost = 3348.84 - 2025.00 = $1323.84

E. Profitability Index = Sum of all PVs / Initial cost = 3348.84 / 2025 = 1.65

F. MIRR = (Sum of FV of all positive cash flows / Sum of PV of all negative cash flows) ^(1/n) -1

FV of positive cash flow = Cft X (1+k)^ (time frame for project -t)

where CFt = Cash flow in year t

K = Reinvestment rate (1%)

t is the year

For example, FV of positive cash flow in year 6 = 392.59 x (1+1%)^(10 -6) = $408.53

MIRR = (4107.32 / 2025.00) ^ (1/10) -1 = 7.328%