(4) a) A firm plans an investment outlay of $1 million 5 years from now. The cur

Question

(4) a) A firm plans an investment outlay of $1 million 5 years from now. The current interest rate is 10% per annum. How much must the firm set aside each year to meet its financial goal?
b) Suppose a firm decides to borrow $500,000 now to implement its investment plan. Assume that repayment will be made in equal annual installments over the next 6 years at the current interest rate of 8%. Determine the amount to be paid each year.

c) Assume the firm in part(b) of this question decides to negotiate the deferment of the first installment until the end of the second period without change in the number of years in the contract. Find the yearly installment payment during the remaining years of the contract such that the bank earns the same level of profit as in part(b)

Explanation / Answer

(a)
r = 10%
n = 5 years

Future value of annuity FV = 1000000 = A*[(1+r)^n - 1]/r
Annual installment to be set aside = A
= FV/([(1+r)^n - 1]/r)
= 1000000*10%/[(1+10%)^5 - 1]
= 163,797.48

(b)
r = 8%
n = 6 years

Present value of annuity PV = 500000 = A*[1-(1+r)^-n]/r
Annual installment = A
= PV/([1-(1+r)^-n]/r)
= 500000*8%/[1-(1+8%)^-6]
= 108,157.69

(c)
PV = 500000
PV of (installment 1 after two years + 5 year annuity starting one year late)

= A/(1+8%)^2 + {A*([1-(1+r)^-n]/r)}/(1+r)
= 0.8573388A + 3.6969537A
= 4.5542925A

A = 500000/4.5542925
= 109786.53

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