Question

1. Corp10 is buying custom-built machinery with a contract purchase price of $943,420. The manufacturer has offered the company a payment plan that would require five annual beginning-of-year payments of $200,000 each.

   1. If the company accepts the offer, what will be the total amount of interest expense it will incur over

      the five-year life of the loan?

   2. If the company can buy the machinery outright by obtaining outside financing elsewhere at 2%,

      should it do or should it accept the manufacturer’s offer instead? Explain briefly?

Answer 1

Answer :-

In order to evaluate the best option, we need to compute the implicit interest rate on offer giving by the manufacturer. Same can be calculated using the below formulae :-

Present value of Annuity ​= PMT x ((1 – (1 / (1 + r) ^ -n)) / r)

• P = the present value of annuity
• PMT = the amount in each annuity payment (in dollars)
• R= the interest or discount rate
• n= the number of payments left to receive

$ 943,420 = $ 200,000 x ((1 – (1 / (1 + r) ^ -5)) / r)

By Solving the above, you will get the implicit Interest rate of 1.973%.

Schedule also provided below :-

Sno	Opening balance	Principal	Interest	Total	Closing balance
1	9,43,420	1,81,383	18,617	2,00,000	7,62,037
2	7,62,037	1,84,962	15,038	2,00,000	5,77,075
3	5,77,075	1,88,612	11,388	2,00,000	3,88,464
4	3,88,464	1,92,334	7,666	2,00,000	1,96,129
5	1,96,129	1,96,130	3,870	2,00,000	-

Total Interest paid = $ 56, 580

Under Loan, total interest paid is $ 57, 384

Sno	Opening balance	Principal	Interest @ 2%	Total	Closing balance
1	9,43,420	1,81,132	18,868	2,00,000	7,62,288
2	7,62,288	1,84,754	15,246	2,00,000	5,77,534
3	5,77,534	1,88,449	11,551	2,00,000	3,89,085
4	3,89,085	1,92,218	7,782	2,00,000	1,96,867
5	1,96,867	1,96,063	3,937	2,00,000	-

Evaluation of options

Sno.	Particulars	Amount
1	Amount of Interest Payable if company accepts the offer	$       56,580
2	Amount of Interest Payable if company avails the loan elsewhere	$       57,384
3	Total Savings if accepted the offer (2-1)	$             804

On the basis of above, we can conclude that interest under offer is less than the loan availed rate. Therefore, offer should be accepted.