Question

Under the terms of a contract, the following payments are guaranteed: $100  000 payable immediately. $75  000 per year for 5 years, payable in equal monthly instalments of $6250 at the end of each month. $50  000 per year, payable annually at the end of the 6th through the 10th years. If interest is at 5% compounded annually, determine the discounted value at the beginning of the 4th year of the remaining payments due under the contract.

Answer 1

Amount receivable, at the beginning of 4th year:

Stream 1: for year 4 & 5: monthly $6250

Stream 2: from years 6 to 10: annually $50,000

Value of stream 1 cashflows at the beginning of year 4:

Monthly amount (PMT) = $6250

Interest rate (I) = 5%/12 = 0.4167% p.m.

number of monthly payments receivable (N) = 24

Value of stream 1 cashflows at the beginning of year 4 (PV) = ?

Using financial calculator or PV function in excel

Value of stream 1 cashflows at the beginning of year 4 (PV) = $ 142,461.86

Value of stream 2 cashflows at the beginning of year 4:

Annual Amount (PMT) = $ 50000

Interest rate (I) = 5% p.a.

number of annual payments receivable (N) = 5

Value of annual payments received at the beginning of year 6 (PV) = ?

Using financial calculator or PV function in excel

Value of annual payments received at the beginning of year 6 (PV) = $ 216,473.83

Value of stream 2 cashflows at the beginning of year 4 = Value at the beginning of year 6 / (1+i)²

Value of stream 2 cashflows at the beginning of year 4 = 216,473.83 / (1+5%)² = $196,348.15

Discounted value at the beginning of the 4th year of the remaining payments due under the contract = $ 142,461.86 + $196,348.15

Discounted value at the beginning of the 4th year of the remaining payments due under the contract = $ 338,810.01

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