Question

Smith Construction Inc. has just purchased several major pieces of road building equipment. Because the purchase price is so large, the supplier is giving Smith the option of choosing among three payment plans:

Option 1 - $600,000 immediately in cash;

Option 2 - $200,000 down payment now and $65,000 per year for each of the next 12 years beginning at the end of the current year;

Option 3 - $90,000 at the end of each of the next 14 years.

Please assume that the cost of capital for Smith Construction is 12%.

Answer 1

We need to determine Present value cash outflow of each option-
Least cash outflow will be preferred
Option 1.
Present value cash outflow is the immediate cash payment which is-	$600,000
Total Present Value of cash outflow	$600,000
Option 2.
Down payment	$200,000
Add: Present value of $65,000 to be paid for 12 years
(Payment starts from end of the current year)
(Cost of capital is 12% which is used to calculate present value)
Present value annuity factor for 12 years at 12% = 6.1939
Hence present value =6.1939*65,000	$402,604
Total Present Value of cash outflow	$602,604
Option 3.
Present value of $90,000 to be paid for next 14 years
(Payment starts from end of the current year)
(Cost of capital is 12% which is used to calculate present value)
Present value annuity factor for 14 years at 12% = 6.6276
Hence present value =6.6276*90,000	$596,484
Total Present Value of cash outflow	$596,484

Conclusion- Option 3 is better than other options since it gives least present value cash outflow, which is $596,484.

Present value annuity factor table is given below for reference-

Year	PV factor	Present value Annuity factor for 12 years and 14 years at 12%
1	0.8929
2	0.7972
3	0.7118
4	0.6355
5	0.5674
6	0.5066
7	0.4523
8	0.4038
9	0.3605
10	0.3219
11	0.2874
12	0.2566	6.1939
13	0.2291
14	0.2046	6.6276

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