Question

Suppose a government has to make the following payments to another government, in perpetuity.

• The first payment is made on 1 July 2020, and is equal to $1 million;
• All subsequent payments are made on the first of each month, but increasing at an inflation rate of 1% every 3 months.
• That is, the payments on 1 August and 1 September are also $1 million each, but the payments on 1 October, 1 November, and 1 December 2020 are $1.01 million each, the payment on 1 January 2021 is equal to $1,020,100, and so on.

1. Assuming an interest rate of 0.25% per annum, and including the value of the payment just made on 1 September 2079, use Excel to calculate the accumulated value of the above payments as at 1 September 2079. DO NOT hand in any excel workings.

Answer: ___________________________________ [2 marks]

2. Complete the 8 missing entries labelled ‘?’ in the following table, using your cashflow projection from Excel.– just complete the table below. [8 marks]

Time (month)	Date	Payment
0	1 July 2020	$1,000,000
1	1 August 2020	$1,000,000
127	?	?
?	1 June 2046	?
?	1 August 2079	?
?	1 September 2079	?

3. Suppose that the inflation rate is now not 1% per quarter at the end of each quarter, but 4% once per year, at the end of each year ending 1 July. Describe how you expect this to change your answer to (a) – does it increase, decrease, or stay the same? Give a reason for your answer. [2 marks]

4. The government making these payments is now concerned about a rapidly changing economic environment. It now expects inflation to be 1.555% per quarter, and interest rates to be 4.25% per year. What now is the accumulated of the above payments as at 1 September 2079? Give your answer to the nearest $million. [you do not need to show working, and DO NOT hand in any excel workings] [2 marks]

Answer 1

a. Accumulated value of the above payments as at 1 September 2079 will be $2,872 Million ($2,872,257,661). This is estimated basis the assumption that 0.25% interest per annum will be applied monthly at 0.0208% per month and is applied at end of the month. Thus, the 1st payment of $1Million on 1st Jul 2020 will earn interest on 1st Aug 2020.

a. Table below:

Time (month)	Date	Payment ($)
0	1 Jul 2020	1,000,000
1	1 Aug 2020	1,000,000
127	1 Feb 2031	1,519,106
311	1 Jun 2046	2,787,353
709	1 Aug 2079	10,469,711
710	1 Sep 2079	10,469,711

a. The answer to above will decrease if the inflation is at 4% per annum instead of 1% per quarter. 1% per quarter when annualised works to 4.06% (as the percentage will be calculated on the sum after the inflation). Since 4% per annum is less than 4.06%, answer to above will decrease. Thus, accumulated value of the above payments as at 1 September 2079 will be $2,765 Million ($2,765,426,889)

a.If the interest rate is  4.25% per annum (monthly 0.3542%) and inflation is 1.555%, accumulated value of the above payments as at 1 September 2079 will be $7,308 Million ($7,307,561,146)