Problem $13-33($LO $6)$

Analyze investment alternatives based on probabilities

Ace Trucking Company is considering buying $50$ new diesel trucks that are $15$ percent more fuel$-$efficient than

the ones the firm is now using. Mr$.$ King, the president, has found that the company uses an average $30$ million

litres of diesel fuel per year at a price of $$1\mathrm{.}08$ per litre. If he can cut fuel consumption by $15$ percent,

he will save $$4,860,000$ per year.

Mr$.$ King assumes that the price of diesel fuel is an external market force he cannot control and any increased

costs of fuel will be passed on to the shipper through higher rates. If this is true, then he would save more

money as the price of diesel fuel rises $($at $$1\mathrm{.}215$ per litre, he would save $$5,467,500$ in total if he buys the new

trucks$).$

Mr$.$ King has come up with two possible forecasts as shown below $-$ each of which he believes has about a

$50$ percent chance of coming true. Under assumption one, diesel prices will stay relatively low; under

assumption two, diesel prices will rise considerably.

Fifty new trucks will cost Ace Trucking $$13\mathrm{.}25$ million. They will qualify for a $30$ percent CCA. The firm has a tax

rate of $30$ percent and a cost of capital of $11$ percent.

a$.$ First compute the yearly expected cost of diesel fuel for both assumption one $($relatively low prices$)$ and

assumption two $($high prices$)$ from the forecasts below.

Forecast for assumption one:

Price of Diesel Fuel per Litre

Probability Year $1$ Year $2$ Year $3$

$0\mathrm{.}10$ $$0\mathrm{.}68$ $$0\mathrm{.}81$ $$0\mathrm{.}95$

$0\mathrm{.}200\mathrm{.}810\mathrm{.}951\mathrm{.}08$

$0\mathrm{.}300\mathrm{.}951\mathrm{.}081\mathrm{.}22$

$0\mathrm{.}201\mathrm{.}081\mathrm{.}221\mathrm{.}35$

$0\mathrm{.}201\mathrm{.}221\mathrm{.}341\mathrm{.}49$

Forecast for assumption two:

Price of Diesel Fuel per Litre

Probability Year $1$ Year $2$ Year $3$

$0\mathrm{.}10$ $$1\mathrm{.}22$ $$1\mathrm{.}35$ $$1\mathrm{.}76$

$0\mathrm{.}301\mathrm{.}351\mathrm{.}492\mathrm{.}03$

$0\mathrm{.}401\mathrm{.}762\mathrm{.}032\mathrm{.}43$

$0\mathrm{.}202\mathrm{.}032\mathrm{.}302\mathrm{.}70$

b$.$ What will be the dollar savings in diesel expenses each year for assumption one and for assumption two?

c$.$ Find the increased cash flow after taxes for both forecasts.

d$.$ Compute the net present value of the truck purchases for each fuel forecast assumption and the combined

net present $($that is$,$ weigh the NPVs by $\mathrm{.}5).$

e$.$ If you were Mr$.$ King, would you go ahead with this capital investment?

f$.$ How sensitive to fuel prices is this capital investment?

Solution

Problem $13-33($LO $6)$

Instructions

Using the various templates setup for each part, enter formulas and cell references to solve the problem.

a$.$ Using the template below, compute the yearly expected cost of diesel fuel for both assumption one $($relatively

low prices$)$ and assumption two $($high prices$).$