Wendell’s Donut Shoppe is investigating the purchase of a new $34,600 donut-maki

Question

Wendell’s Donut Shoppe is investigating the purchase of a new $34,600 donut-making machine. The new machine would permit the company to reduce the amount of part-time help needed, at a cost savings of $6,500 per year. In addition, the new machine would allow the company to produce one new style of donut, resulting in the sale of 2,500 dozen more donuts each year. The company realizes a contribution margin of $1.60 per dozen donuts sold. The new machine would have a six-year useful life.  

What would be the total annual cash inflows associated with the new machine for capital budgeting purposes?

Find the internal rate of return promised by the new machine to the nearest whole percent.

In addition to the data given previously, assume that the machine will have a $14,000 salvage value at the end of six years. Under these conditions, compute the internal rate of return to the nearest whole percent. (Round discount factor(s) to 3 decimal places.)

Required: 1.

What would be the total annual cash inflows associated with the new machine for capital budgeting purposes?

Explanation / Answer

Answer:

In the absence of Depreciation method and tax rate, depreciation is not considered in calculating Annual Cash Inflow. If it is required than calculation and amount of all the answer will be changed accordingly.

1) Calculation of total annual cash inflows associated with the new machine

Particulars

Amount

A.

Annual Cost Saving in part time help

$6,500

B.

Annual Increase in Revenue from sale of Donuts (2,500 x $1.60)

$4,000

Total Annual Cash Inflows (A+B)

$10,500

Notes:

2) Calculation of Internal Rate of Return

Internal Rate of return is a discounting rate which is calculated by using following steps:

Step 1: Calculated NPV by taking a discounting rate (discounting rate can be assumed by discretionary)

Step 2:

Step 3: Apply formula

IRR = Lower Rate + [NPV at Lower Rate/(NPV at lower rate – NPV at higher rate)] x (Higher Rate – Lower Rate)

Calculation of IRR

Net Present Value = PV of Cash Inflows – PV of Cash Outflows

PV of Cash Outflows = $34,600 (Cost of New Machine)

PV of Cash Inflows = Annual Cash Inflow x PVIFA (Rate, n) + Salvage Value x PVIF (Rate, n)

Now, we calculate NPV by using 15% discounting rate

PV of Cash Inflows = $10,500 x PVIFA (15%, 6) + 0 = $10,500 x 3.784 = $39,732

NPV at 15% = $39,732 - $34,600 = $5,132

Now, we calculate NPV at higher rate than 15% i.e. 21%

PV of Cash Inflow at 21% = $10,500 x 3.245 = $34,073

NPV at 21% = $34,073 - $34,600 = -$527

By applying formula from Step – III

IRR = 15% + [($5,132 / $5,132 – (-$527)] x (21% - 15%)

IRR = 15% + (0.907 x 6%) = 15% + 5.442% = 20.442% or in whole number 21%

3) If machine have salvage value $14,000 at the end of 6th year.

PV of Cash Inflows at 20% = ($10,500 x 3.326) + $14,000 x 0.335 = $34,923 + $4,690 = $39,613

NPV at 20% = $39,613 - $34,600 = $5,013

PV of Cash Inflow at 25% = ($10,500 x 2.951) + (0.262 x $14,000) = $30,985 + $3,668 = $34,653

By above calculation, it is clear that at 25% discounting rate, PV of Cash Inflow will become equal to PV of Cash Inflow…so there is no need to further calculation..

In this case IRR is25%

Particulars

Amount

A.

Annual Cost Saving in part time help

$6,500

B.

Annual Increase in Revenue from sale of Donuts (2,500 x $1.60)

$4,000

Total Annual Cash Inflows (A+B)

$10,500

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