Question

Five years ago, a company was considering the purchase of 77 new diesel trucks that were 15.45% more fuel-efficient than the ones the firm is now using. The company uses an average of 10 million gallons of diesel fuel per year at a price of $1.25 per gallon. If the company manages to save on fuel costs, it will save $1.875 million per year (1.5 million gallons at $1.25 per gallon). On this basis, fuel efficiency would save more money as the price of diesel fuel rises (at $1.35 per gallon, the firm would save $2.025 million in total if he buys the new trucks).

Consider two possible forecasts, each of which has an equal chance of being realized. Under assumption #1, diesel prices will stay relatively low; under assumption #2, diesel prices will rise considerably. The 77 new trucks will cost the firm $5 million. Depreciation will be 25.2% in year 1, 38.48% in year 2, and 36.34% in year 3. The firm is in a 40% income tax bracket and uses a 10% cost of capital for cash flow valuation purposes. Interest on debt is ignored. In addition, consider the following forecasts:

Forecast for assumption #1 (low fuel prices):

Price of Diesel Fuel per Gallon

Prob. (same for each year)

Year 1

Year 2

Year 3

0.1

$0.79

$0.92

$1.01

0.2

$0.99

$1.13

$1.12

0.3

$1.12

$1.2

$1.3

0.2

$1.31

$1.44

$1.44

0.2

$1.4

$1.57

$1.6

Forecast for assumption #2 (high fuel prices):

Price of Diesel Fuel per Gallon

Prob. (same for each year)

Year 1

Year 2

Year 3

0.1

$1.22

$1.51

$1.7

0.3

$1.3

$1.71

$2.02

0.4

$1.82

$2.33

$2.49

0.2

$2.21

$2.5

$2.79

Required: Calculate the percentage change on the basis that an increase would take place from the NPV under assumption #1 to the probability-weighted (expected) NPV.

Answer

% Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places (for example: 28.31%).

Note: The educational purpose of this problem targets the students’ ability to read + follow instructions.

Further Information (solution steps):

Step (1): Calculate the annual expected price of diesel per gallon under each assumption, based on the probabilities outlined in the inputs section.

Step (2): Using the annual expected fuel prices calculated in step (1), determine the increase in annual savings created by the proposed efficiency for each assumption.

Step (3): Find the increased cash flow after taxes (CFAT) for both forecasts, based on the annual increase in fuel savings determined in step (2) as the increase in earnings before depreciation and taxes (EBDT), and the starting point from which profit is calculated for each assumption. As part of this step, you must establish annual depreciation (remember: depreciation is a noncash charge).

Step (4): Considering the increased annual CFAT produced in step (3), calculate the NPV of the truck purchases for each assumption, based on the discount rate (cost of capital) indicated in the inputs section

Step (5): In view of the outcomes produced in step (4), estimate the combined NPV weighed by the probability of each assumption.

Step (6): Finally, calculate the percentage difference hypothesizing that an increase took place starting from the NPV for assumption #1 to the combined NPV worked out in step (5).

Q1) you will notice as we proceed that the steps are truly consecutive (none can be fulfilled before the step before is complete). therefore, there is truly nothing about the question that's difficult. it's a long question, not a difficult one.

NOTE #1: IT IS EXTREMELY IMPORTANT THAT YOU DO NOT ROUND INTERMEDIATE CALCULATIONS BECAUSE THIS QUESTION IS DESCRIBED BY SEVERAL STEPS … ROUNDING UPON ROUNDING CREATES OVER-ROUNDING AND THEREBY A CONSIDERABLE DIFFERENCE BY THE TIME YOU REACH THE FINAL STEP.

NOTE #2: 10M GALLONS ARE THE SAME ACROSS ALL EXAM SCRIPT FORMS. SAVINGS % VARY.

NOTE #3: IT IS HIGHLY RECOMMENDED THAT YOU DO NOT USE ZEROS AS YOU MULTIPLY × 10 M GALLONS. IT WILL ONLY MAKE YOUR WORKINGS MORE CONFUSING. IF SOMETHING GOES WRONG AT A LATER STAGE, IT WILL BE MUCH EASIER FOR YOU TO IDENTIFY WHERE EXACTLY.

NOTE #4: AS CAN BE OBSERVED IN THE CALCULATIONS ABOVE, SAVINGS ARE CONVERTED FROM % TERMS TO $ TERMS. EACH OF THESE $ ANNUAL SAINGS IS A DIFFERENTIAL (ANNUAL) VALUE IN AN OF ITSELF, DESCRIBED BY A POSITIVE SIGN. AFTER ALL, SAVINGS ARE INFLOWS.

NOTE #5: INTEREST EXPENSE IS IGNORED ACROSS ALL EXAM SCRIPT FORMS.

NOTE #6: THE $5M COST IS THE SAME ACROSS ALL EXAM SCRIPT FORMS. ANNUAL DEPRECIATION % VARIES.

NOTE #7: IMAGINE THAT BY NOW YOU ARE DEALING WITH ZEROS AFTER MULTIPLYING × 10 M GALLONS EARLIER. NOW, YOU WOULD BE FURTHER MULTIPLYONG × $5M COST…

NOTE #8: REMEMBER THAT WE ARE OUTLINING DIFFERENTIAL VALUES HERE AS EXPLAINED IN NOTE #4, THAT’S WHY EACH AFTER-TAX CASH FLOW (ATCF) IS OBSERVED AS AN INCREASE.

NOTE #9: ALSO RECALL FROM PROVISION (ii) ABOVE THAT $ ANNUAL DEPRECIATION MUST BE ADDED BACK TO THE INCREASE IN NET INCOME (HERE, ATCF) ON ACCOUNT THAT DEPRECIATION IS A NON-CASH EXPENSE ITEM.

NOTE #10: IT IS QUITE LIKELY THAT THE NPV FOR THE LOW FUEL PRICES SCENARIO IS GOING TO BE NEGATIVE (IN OTHER WORDS, OUTFLOWS > INFLOWS). THIS IS VERY IMPORTANT TO KEEP IN MIND FOR THE UPCOMING STEP.

NOTE #11: EVEN THOUGH YOU ARE FREE TO USE THE APPENDIX, QUITE CLEARLY, APPENDIX B IN THIS CASE, AS WE ARE DEALING WITH SINGLE AMOUNTS. HOWEVER, IT IS HIGHLY RECOMMENDED THAT YOU USE THE FORMULA ON ACCOUNT THAT YOU SHOULD NOT BE ROUNDING INTERMEDIATE CALCULATIONS. BESIDES, WE ARE ONLY TALKING ABOUT 3 YEARS ONLY. 

NOTE #12: BECAUSE EACH SCENARIO HOLDS A 50% CHANCE OF TAKING PLACE, THE GEOMETRIC MEAN IN THIS PARTICULAR CASE = THE ARITHMETIC MEAN, SUCH THAT BOTH NET PRESENT VALUES CAN BE ADDED, THEN ÷ 2. 

Answer 1

Please hit like if this helps, comment for any further queries.

Assumption 1
									(A)	(B)		(C)	(D)		(E) = (A) - (B) + (D)	(F)
Year	0.1	0.2	0.3	0.2	0.2		Probable Price for the Year		Fuel Savings	Tax on Fuel Savings		Depreciation Expense	Tax Saved on Depreciation		Net Savings in Fuel	NPV of (E)
Year 1	$       0.79	$       0.99	$                1.12	$       1.31	$       1.40		1.155		$   1,784,475	$       713,790		$     1,260,000	$         504,000		$            1,574,685	$     1,431,532
Year 2	$       0.92	$       1.13	$                1.20	$       1.44	$       1.57		1.28		$   1,977,600	$       791,040		$     1,924,000	$         769,600		$            1,956,160	$     1,616,661
Year 3	$       1.01	$       1.12	$                1.30	$       1.44	$       1.60		1.323		$   2,044,035	$       817,614		$     1,816,000	$         726,400		$            1,952,821	$     1,467,183
															Net Benefit in 3 years will be =	$     4,515,376
															Less:- Cost of 77 new Trucks	$    -5,000,000
Assumption 2														NPV under assumption 1	$       -484,624
Year	0.1	0.3	0.4	0.2
Year 1	$       1.22	$       1.30	$                1.82	$       2.21			1.682		$   2,598,690	$   1,039,476		$     1,260,000	$         504,000		$            2,063,214	$     1,875,649
Year 2	$       1.51	$       1.71	$                2.33	$       2.50			2.096		$   3,238,320	$   1,295,328		$     1,924,000	$         769,600		$            2,712,592	$     2,241,812
Year 3	$       1.70	$       2.02	$                2.49	$       2.79			2.33		$   3,599,850	$   1,439,940		$     1,816,000	$         726,400		$            2,886,310	$     2,168,527
															Net Benefit in 3 years will be =	$     6,285,988
															Less:- Cost of 77 new Trucks	$    -5,000,000
															NPV under assumption 2	$     1,285,988

NPV under assumption 1	$       -484,624
NPV under assumption 2	$     1,285,988
Average NPV	$         400,682
% Change in Assumption 1 and Average NPV	-183%