Question

Required information [The following information applies to the questions displayed below.] Wendell's Donut Shoppe is investigating the purchase of a new $18,600 donut-making machine. The new machine would permit the company to reduce the amount of part-time help needed, at a cost savings of $3,800 per year. In addition, the new machine would allow the company to produce one new style of donut, resulting in the sale of 1,000 dozen more donuts each year. The company realizes a contribution margin of $1.20 per dozen donuts sold. The new machine would have a six-year useful life. (Ignore income taxes.) Solve this question using your financial calculator or Excel, NOT the tables in the chapter. Requirement 2: Find the internal rate of return promised by the new machine. (Round your answer to two decimal places. Omit the "%" sign in your response.) Internal rate of return %

Answer 1

Internal rate of return is the rate at which Present Value of Cash Flows generated from the investment equals the investment value. In other words, Internal rate of return is the rate at which NPV of the project becomes zero.

Initial Investment = $18,600

Cash Flows every year = $3,800 + (1,000 x 1.2) = $5,000

Let us first calculate NPV using 10% rate of return:

Since NPV at 10% is positive, so IRR is greater than 10%. Now let us calculate NPV using 18% rate.

Since NPV at 18% rate is negative, therefore NPV is somewhere between 10% and 18%.

NPV difference = 3,176 - (-1,112) = 4,288

Rate Difference = 18% - 10% = 8%

When NPV difference is 4,288, rate difference is 8%. Therefore,

To cover NPV difference of 3,276, rate difference = (8 / 4,288) x 3,176 =5.92

Therefore required Internal Rate of Return = 10 + 5.92 = 15.92