18-14 (Cost of a term loan) Temple Freight Forwarding Company needs $300 000 to

Question

18-14 (Cost of a term loan) Temple Freight Forwarding Company needs $300 000 to finance the construction of several prefabricated metal warehouses. The firm that manufactures the warehouses has offered to finance the purchase with a $50 000 down-payment followed by five annual instalments of $69 000 each. Alternatively, Temple’s bank has offered to lend the firm $300 000 to be repaid in 10 half-yearly instalments based on a nominal annual rate of interest of 16%. Finally, the firm could finance the needed $300 000 through a loan from a finance broker requiring a single lump-sum payment of $425 000 in five years.

(a) What is the effective annual rate of interest on the loan from the warehouse manufacturer?

(b) What will the annual payments on the bank loan be?

(c) What is the annual rate of interest for the term loan from the finance broker?

(d) Based on cost considerations only, which source of financing should Temple select?

Explanation / Answer

a. In case of the loan of warehouse manufacturer, the effective annual interest rate will make the present value of the $50,000 downpayment and the present value of the 5 annual installments of $69,000 equal to the amount of $300,000.

Let the effective annual interest rate be = x

Thus,

50,000+69,000/(1+x)+69,00/(1+x)^2+69,000/(1+x)^3+69,000/(1+x)^4+69,000/(1+x)^5 = 300,000

or, 69,000/(1+x)+69,00/(1+x)^2+69,000/(1+x)^3+69,000/(1+x)^4+69,000/(1+x)^5 = 250,000

solving the above equation using a trial and error approach, we get x as 11.79467%

b. Bank loan: nominal annual interest rate = 16%. It will translate into a rate of 16/2 = 8% per half year. There will be 10 such payments. Let each payment be x. This is an annuity. Annuity factor for r = 8% and n = 10 is 6.71008 (from the present value of an annuity table).

Thus, x*6.71008 = 300,000 or x = 44,708.85. This is the payment being made every 6 months. Annual payment will be = 44708.85*2 = $89,417.69

c. term loan from finance broker: Here a single lump sum payment is made after 5 years. This the future value.

Thus: future value/(1+r)^5 = present value or 425,000/(1+r)^5 = 300,000

or (1+r)^5 = 425,000/300,000 = 1.4167

1+r = 1.072145

or r = 1.072145 - 1 = 0.072145 or 7.2145%

d. The cost of financing is the lowest for the finance broker @ 7.2145% and hence this should be used.

Year Amount 1+x PV 0 50000 1.117947 50000 1 69000 61720.3 2 69000 55208.62 3 69000 49383.95 4 69000 44173.8 5 69000 39513.33 Total 300000

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