Exercise 13-3 Internal Rate of Return [LO13-3] Wendell’s Donut Shoppe is investigating the purchase of a new $42,800 donut-making machine. The new machine would permit the company to reduce the amount of part-time help needed, at a cost savings of $5,700 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 $1.50 per dozen donuts sold. The new machine would have a six-year useful life. Click here to view Exhibit 138-1 and Exhibit 13B-2, to determine the appropriate discount factor(s) using tables. Required: 1. What would be the total annual cash inflows associated with the new machine for capital budgeting purposes Annual savings in part-time help Added contribution margin from expanded sales Annual cash inflows 2. Find the internal rate of return promised by the new machine to the nearest whole percent. Internal Rate of Return Choose Numerator: / Choose Denominator: Factor Number of years Internal rate of return Factor
Expert Answer
1 | Annual cash flows from new machine | |
Savings in part time help | $5,700 | |
Contribution margin from expanded sales (2,500*$1.5) |
$3,000 | |
Annual Cash flows | $8,700 | |
2 | Internal rate of return | |
At IRR present value of cash inflows=Present value of cash outflows | ||
Present value of cash outflows= $42,800 | ||
Present value of cash inflows = (Annual cash flows *Annuity factor at IRR for 6 years) | ||
Annuity factor = present value of cash outflows/Annual cash outflows | ||
($42,800/$8,700) = 4.92 | ||
Annuity factor for 6 years equal to 4.92 at 6% | ||
Therefore IRR = 6% |
3 | Internal rate of return | ||
Assume IRR = 10% and check | |||
Year | Cash flows | P.V factor @ 10% | Discounted cash flows |
1 | $8,700 | 0.909 | $7,909.17 |
2 | $8,700 | 0.826 | $7,189.68 |
3 | $8,700 | 0.751 | $6,536.31 |
4 | $8,700 | 0.683 | $5,942.10 |
5 | $8,700 | 0.621 | $5,401.83 |
6 | $8,700 | 0.565 | $4,911.15 |
6 | Salvage value $16,280 | 0.565 | $9,190.06 |
P.V of cash inflows | $47,080.30 | ||
Assume IRR = 13% and check | |||
Year | Cash flows | P.V factor @ 13% | Discounted cash flows |
1 | $8,700 | 0.8850 | $7,699.12 |
2 | $8,700 | 0.7831 | $6,813.38 |
3 | $8,700 | 0.6931 | $6,029.54 |
4 | $8,700 | 0.6133 | $5,335.87 |
5 | $8,700 | 0.5428 | $4,722.01 |
6 | $8,700 | 0.4803 | $4,178.77 |
6 | Salvage value $16,280 | 0.4803 | $7,819.59 |
P.V of cash inflows | $42,598.27 | ||
P.V of cash outflows | $42,800 | ||
Therefore p.v of inflows almost equal to p.v of outflows so IRR is 13% | |||
Ans) | IRR=13% |