Cousin\'s Salted Snack Company is considering two possible investments: a delive
ID: 2494642 • Letter: C
Question
Cousin's Salted Snack Company is considering two possible investments: a delivery truck or a bagging machine. The delivery truck would cost $53,714.90 and could be used to deliver an additional 51,000 bags of pretzels per year. Each bag of pretzels can be sold for a contribution margin of $0.58. The delivery truck operating expenses, excluding depreciation, are $0.79 per mile for 17,000 miles per year. The bagging machine would replace an old bagging machine, and its net investment cost would be $42,525.00. The new machine would require three fewer hours of direct labor per day. Direct labor is $15 per hour. There are 250 operating days in the year. Both the truck and the bagging machine are estimated to have six-year lives. The minimum rate of return is 19%. However, Cousin's has funds to invest in only one of the projects.
a. Compute the internal rate of return for each investment. Use the above table of present value of an annuity of $1. If required, round your present value factor answers to three decimal places and internal rate of return to the nearest percent.
Present Value of an Annuity of $1 at Compound Interest Year 6% 10% 12% 15% 20% 1 0.943 0.909 0.893 0.870 0.833 2 1.833 1.736 1.690 1.626 1.528 3 2.673 2.487 2.402 2.283 2.106 4 3.465 3.170 3.037 2.855 2.589 5 4.212 3.791 3.605 3.352 2.991 6 4.917 4.355 4.111 3.784 3.326 7 5.582 4.868 4.564 4.160 3.605 8 6.210 5.335 4.968 4.487 3.837 9 6.802 5.759 5.328 4.772 4.031 10 7.360 6.145 5.650 5.019 4.192Explanation / Answer
1. Delivery truck:
Contribution margin 51,000 x 0.58 = $ 29,580
Expenses of operating the truck 17,000 x 0.79 = $ 13,430
Therefore, net operating cash flows per annum $ 16,150
At 19% required return PVIFA for 6 years is 3.410 ( Can be calculated by interpolation)
To calculate Internal rate of return, first calculate the fake payback value.
Fake payback value is Initial investment / annual cash flows =53,714.90 / 16,150 = 3.326
This value exactly corresponds with the 6 year PVIFA value at 20%.
Hence the internal rate of return is 20%
2. Bagging Machine
Incremental cash flows per year = $ ( 3 x 15 x 250) = $ 11,250.
Fake payback value = Initial investment / annual cash flows = 42,525 / 11,250 = 3.78
If we consult the given table at 6 years, we find that the value nearest to the fake payback value is 3.784 at 15%. Therefore, the internal rate of return for bagging machine is 15% approx.