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Class Test 9 - This is used in IAS 282 an actuarial science module at TUKS/UP during second

This is used in IAS 282 an actuarial science module at TUKS/UP during...
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Actuarial Science (IAS 282)

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Department Actuarial Science University of Pretoria

Page 1 of 2

Financial Mathematics 282

Class Test 9

Date: 13 October 2022 Marks: 12 marks Time: 22 minutes

Question 2 [9 marks]

Ms Anna read an article about warehouses and e-commerce. On 1 January 2022, she started a project with the following cashflows:  Construction will start on 1 July 2022. Construction costs are expected to be R300 000 per annum, payable semi-annually in advance for a year.  A quarterly expense of R45 000 starting three months after construction costs cease. Every payment after the first is expected to be R5 000 more than the preceding one.  Income of R700 000 a year, payable monthly in advance starting immediately when construction costs cease. Anna plans on gifting the business to her friend Tristan on 30 June 2024. Assume all cashflows will stop then.

Consider the following inflation index (assume that the index values are given as at the start of every quarter):

Year Quarter 1 Quarter 2 Quarter 3 Quarter 4 2022 108 114 121 126. 2023 130 138 149 163. 2024 172 189 192 200.

a) Calculate the present value of the income on 1 January 2022 assuming a gross nominal yield of 12% per annum. [1]

Department Actuarial Science University of Pretoria

Page 2 of 2

Anna wants to take inflation into account and asks you to make use of the above index when calculating the NPV of her investment. Use the answer in (a) for the present value of the income in your calculation of the NPV, however in respect of the construction costs and expenses, you will have to take inflation into account. Anna requires a real yield of 8% p. on her investment.

b) Given the above. calculate the NPV of Anna’s project on 1 January 2022. [6]

c) Without any further calculations, how would your answer differ to what you obtained in (b) if you had calculated the NPV by not taking inflation into consideration when calculating the construction costs? Assume the required real yield is still 8% p. [2]

Question 3 [3 Marks]

Tylene has a son aged nine, exactly, on 1 January 2021. She would like to save up for her son’s tuition fees which must be paid on each 1 January of her son’s three years at university (when her son will turn 19, 20 and 21). The formula 32000[1]𝑛 represents the real cashflows she expects to receive at the start of each year at university in rand. The start of each university year is represented by 𝑛 i. 𝑛 = 0,1,2.

Tylene can earn an effective real interest rate on her investment portfolio of 9% per annum for the next six years, and 4% per annum, thereafter. The inflation rate is expected to remain constant at 5% per annum for the foreseeable future.

Calculate the amount of money Tylene should invest on 1 January 2021 to be able to pay the expected real fees (cashflows as per formula) as they fall due assuming that she can earn an effective real interest rate as stated above.

END OF CLASS TEST

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Class Test 9 - This is used in IAS 282 an actuarial science module at TUKS/UP during second

Course: Actuarial Science (IAS 282)

12 Documents
Students shared 12 documents in this course

University: University of Pretoria

Was this document helpful?
Department Actuarial Science
University of Pretoria
Page 1 of 2
Financial Mathematics 282
Class Test 9
Date: 13 October 2022
Marks: 12 marks
Time: 22 minutes
Question 2 [9 marks]
Ms Anna read an article about warehouses and e-commerce. On 1 January 2022, she started a
project with the following cashflows:
Construction will start on 1 July 2022. Construction costs are expected to be R300 000
per annum, payable semi-annually in advance for a year.
A quarterly expense of R45 000 starting three months after construction costs cease.
Every payment after the first is expected to be R5 000 more than the preceding one.
Income of R700 000 a year, payable monthly in advance starting immediately when
construction costs cease.
Anna plans on gifting the business to her friend Tristan on 30 June 2024. Assume all cashflows
will stop then.
Consider the following inflation index (assume that the index values are given as at the start of
every quarter):
Year
Quarter 1
Quarter 2
Quarter 3
2022
108.55
114.75
121.86
2023
130.32
138.41
149.96
2024
172.48
189.04
192.43
a) Calculate the present value of the income on 1 January 2022 assuming a
gross nominal yield of 12% per annum. [1]

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