Pisa Pizza Parlor is investigating the purchase of a new $50,000 delivery truck
ID: 2371931 • Letter: P
Question
Pisa Pizza Parlor is investigating the purchase of a new $50,000 delivery truck that would contain specially designed warming racks. The new truck would have a eight-year useful life. It would save $6,500 per year over the present method of delivering pizzas. In addition, it would result in the sale of 2,500 more pizzas each year. The company realizes a contribution margin of $1 per pizza. (Ignore income taxes.)
1)What would be the total annual cash inflows associated with the new truck for capital budgeting purposes?
I know this answer is $9000
2)Find the internal rate of return promised by the new truck. (Round discount factor(s) to 3 decimal places and final answer to the closest interest rate. Omit the "%" sign in your response.)
3) In addition to the data already provided, assume that due to the unique warming racks, the truck will have a $14,000 salvage value at the end of eight years. Under these conditions, compute the internal rate of return(Round discount factor(s) to 3 decimal places and final answer to the closest interest rate. Omit the "%" sign in your response.)
Explanation / Answer
1) Since the company would save $6,500 with the new delivery system (or that costs will be $6,500 less) that will increase the cash inflows by $6,500. The company has a $1 contribution margin per pizza (contribution margin= revenues - cost). So for every pizza sold the company will add $1 to its cash inflow.
Annual cash inflow= $6,500 + 2,500 pizzas sold x $1 contribution margin per pizza
Annual cash inflow= $9,000
2) The internal rate of return is the rate at which the initial cash outflow equals the present value of the cash inflows. The cash flows in this scenario are equal and annual (an annuity) so:
Investment cost = PV of cash flows
50,000 = 9,000 cash flow x present value annuity factor (i=?, n=8)
50,000 / 9,000 = PVA factor (i=?, n=8)
5.556 = PVA factor
From here we scan the present value of an annuity table at n=8 to see which interest rate is closest to the PVA factor:
i=8, n=8 : 5,747
i=9, n=8 : 5.535
Since the table factor for i=9 is closest to our solution the IRR for this scenario is 9.
3) Since the cash inflows in this scenario are uneven, you must either use trial and error or a finacial calculator. The final cash inflow would include the $14,000 salvage value (cash flow 8= $23,000)
via trial and error you would use this formula:
Investment cost = present value of an annuity + present value $1
50,000 = 9,000 x PVA (i=?, n=7*) + 23,000 x PV$1 (i=?, n=8)
*n=7 since the annutiy is only active for the first 7 cash flows
You would have to try an interest rate, insert the table factor and solve the equation to find the interest rate at which the equation balances (or comes as close as possible to balancing). In this case that rate is 12%
50,000 = 9,000 x 4.564 + 23,000 x .404
50,000 = 50368