Question

Brief Exercise 26-11 Kanye Company is evaluating the purchase of a rebuilt spot- welding machine to be used in the manufacture of a new product. The machine will cost $176,000, has an estimated useful life of 7 years, a salvage value of zero, and will increase net annual cash flows by $38,564 What is its approximate internal rate of return? (Round answer to O decimal place, e.g. 125.) Internal rate of return

Answer 1

Answer

• Answer = 12%

• Internal Rate of Return [or IRR] is that interest rate where the present values of future annual cash flows when discounted becomes EQUAL to the Initial Investment cost.
• This means that:

--Present Value of annual cash flows = Initial Cost

OR

--Net Present Value = $ 0, because NPV = Present values of annual cash flows – Initial Cost.

• Present value of annual Cash flows = Annual Cash Flows x Present value of annuity of $ 1 at IRR
• Hence, NPV = (Annual Cash Flows x Present value of annuity of $ 1 at IRR) – Initial Cost

$ 0 = ($ 38,564 x Present value of annuity of $ 1 at IRR) - $ 176,000

0 = (38564 x Present value of annuity of $ 1 at IRR) – 176000

0+176000 = 38564 x Present value of annuity of $ 1 at IRR

176000/38564 = Present value of annuity of $ 1 at IRR

Present value of annuity of $ 1 at IRR = 4.56384….

• Now you have to look into factor table to see which interest rate’s annuity value at 7^th period equals 4.56384….

	8%	9%	10%	11%	12% = ANSWER	13%	14%
1	0.925925926	0.917431193	0.909090909	0.900900901	0.892857143	0.884955752	0.877192982
2	0.85733882	0.841679993	0.826446281	0.811622433	0.797193878	0.783146683	0.769467528
3	0.793832241	0.77218348	0.751314801	0.731191381	0.711780248	0.693050162	0.674971516
4	0.735029853	0.708425211	0.683013455	0.658730974	0.635518078	0.613318728	0.592080277
5	0.680583197	0.649931386	0.620921323	0.593451328	0.567426856	0.542759936	0.519368664
6	0.630169627	0.596267327	0.56447393	0.534640836	0.506631121	0.480318527	0.455586548
7	0.583490395	0.547034245	0.513158118	0.481658411	0.452349215	0.425060644	0.399637323
	5.20637	5.03295	4.86842	4.71220	4.5638 = matches the value	4.42261	4.28830