FM – Nov 2020 – L2 – Q3a – DCF: Specific applications

FM – Nov 2020 – L2 – Q3a – DCF: Specific applications | Discounted cash flow

Calculate the present value of payments under cash and credit purchase options, and recommend the better option.

Question

The directors of PDS Foods Ltd (PDS) are considering two payment options for the purchase of a new cereal processing plant:

Option 1: Cash purchase option
This option requires immediate payment of the full price of the plant. If PDS chooses this option, it will pay the cash price of GH¢800,379 today. PDS plans to raise the required amount by borrowing from a bank. Conso Bank Ghana has offered to lend the cash price to PDS at an annual interest rate of 15% with monthly compounding. The loan, interest, and other charges are to be amortized by even instalments of GH¢27,952.26 each made at the end of each month over the next three years.

Option 2: Credit purchase plan
Under this option, the vendor requires an immediate down payment followed by a series of even payments. If PDS chooses this option, it will be required to pay GH¢50,000 today. This will be followed by the payment of GH¢116,100 at the end of each quarter over the next two years. The interest rate implicit in this credit purchase plan is 20% per annum.

Required:

i) Find the present value of all the payments under the cash purchase option. (5 marks)
ii) Find the present value of all the payments under the credit purchase option. (4 marks)
iii) Which of the two options do you recommend to the company? Explain. (1 mark)

Answer

i) Present value of the payments under the cash purchase option:

The payments PDS will make under the cash purchase option are effectively the payments under the loan arrangement, which form an ordinary annuity:

Where:

PMT = GH¢27,952.26 (Even payment)
Annual interest rate $i$ = 15%
Frequency = 12 (monthly)
Term = 3 years
Number of periods = 3 \times 12 = 36 months

ii) Present value of all the payments under the credit purchase option:
PV of payments = Down payment + PV of instalments (which is an ordinary annuity)
where:
Down payment = 50,000
Even payment (PMT) = GH¢116,100
Annual interest rate $i$ = 20%
Frequency $m$ = 4 (quarterly)
Term $t$ = 2 years
Number of periods $n$ = 2 \times 4 = 8 quarters