DSC1630 ASSIGNMENT 04 2022 UNIQUE NUMBER 632596
Introductory Financial Mathematics …………………………….DSC1630
Semester 1 2022
DSC1630/ Compulsory Assignment: 04 2022 Unique Number: 632596
Due Date: 26 April 2022
Solution Summary
The following is a summary of the correct answers:
Q1 Option 1
Q2 Option 3
Q3 Option 1
Q4 Option 2
Q5 Option 1
Q6 Option 2
Q7 Option 3
Q8 Option 4
Q9 Option 4
Q 10 Option 3
Q 11 Option 3
Q 12 Option 4
Q 13 Option 1
Q 14 Option 4
Q 15 Option 1
1
, DSC1630 ASSIGNMENT 04 2022 UNIQUE NUMBER 632596
Questions 1, 2 and 3 are based on the following situation:
An investment with an initial outlay of R500 000 generates five successive annual
cash inflows of R75 000, R190 000, R40 000, R150 000 and R180 000 respectively.
The cost of capital K is 10% per annum
Question 1
The internal rate of return (IRR) is
[1] 7, 78%.
[2] 21, 3%.
[3] 27, 0%.
[4] 9, 48%.
Notes: Definition of IRR (internal rate of return): The compounded interest rate which, when used to
discount the cash flows, will yield a present value equal to the initial investment.
IRR is used to make accept–reject decisions, and these following criteria are used:
If the IRR is greater than the cost of capital, accept the project.
If the IRR is less than the cost of capital, reject the project.
Steps:
Draw a timeline for the cash flows
𝐼𝑜𝑢𝑡 = R500 000
𝐶1 =75 000 𝐶2 = 190 000 𝐶3 =40 000 𝐶4 =150 000 𝐶5 =180 000
75 000 190 000 40 000 150 000 180 000
Now f (i) = + + + + - 500 000
(1+𝑖) (1+𝑖)2 (1+𝑖)3 (1+𝑖)4 (1+𝑖)5
We must determine i such that f (i) = 0.
Use calculator to solve i
We find that the internal rate of return for the investment is 7.78%. Reject proposal
[Option 1]
2
, DSC1630 ASSIGNMENT 04 2022 UNIQUE NUMBER 632596
Question 2
The net present value (NPV) is approximately
[1] R135 000.
[2] −R135 000.
[3] −R30 523.
[4] R74 500.
Notes; NPV definition: The net present value (NPV) of an investment proposal is the present value of all
future cash inflows (𝑃𝑉𝑖𝑛 ) less the investment outlay (𝐼𝑜𝑢𝑡 )
If the NPV is positive (greater than zero), the proposal may be regarded as acceptable. If it is negative
(smaller than zero), it is not. And if it is zero, the investor will be indifferent.
NPV = 𝑃𝑉𝑖𝑛 - 𝐼𝑜𝑢𝑡
𝐶1 𝐶2 𝐶3 𝐶4 𝐶5
NPV = + + + + - 𝐼𝑜𝑢𝑡
1+𝐾 (1+𝐾)2 (1+𝐾)3 (1+𝐾)4 (1+𝐾)5
75000 190000 40000 150000 180000
= + + + + – 500000
1.1 (1.1)2 (1.1)3 (1.1)4 (1.1)5
= 68181.82 + 157024.79 + 30052.59+ 102452.02+ 111765.84 -500000
= 469477.06 -500000
= - 30 522.94
= -R30 523
If you use the calculator it agrees with this same amount. Therefore reject proposal
[Option 3]
3
Introductory Financial Mathematics …………………………….DSC1630
Semester 1 2022
DSC1630/ Compulsory Assignment: 04 2022 Unique Number: 632596
Due Date: 26 April 2022
Solution Summary
The following is a summary of the correct answers:
Q1 Option 1
Q2 Option 3
Q3 Option 1
Q4 Option 2
Q5 Option 1
Q6 Option 2
Q7 Option 3
Q8 Option 4
Q9 Option 4
Q 10 Option 3
Q 11 Option 3
Q 12 Option 4
Q 13 Option 1
Q 14 Option 4
Q 15 Option 1
1
, DSC1630 ASSIGNMENT 04 2022 UNIQUE NUMBER 632596
Questions 1, 2 and 3 are based on the following situation:
An investment with an initial outlay of R500 000 generates five successive annual
cash inflows of R75 000, R190 000, R40 000, R150 000 and R180 000 respectively.
The cost of capital K is 10% per annum
Question 1
The internal rate of return (IRR) is
[1] 7, 78%.
[2] 21, 3%.
[3] 27, 0%.
[4] 9, 48%.
Notes: Definition of IRR (internal rate of return): The compounded interest rate which, when used to
discount the cash flows, will yield a present value equal to the initial investment.
IRR is used to make accept–reject decisions, and these following criteria are used:
If the IRR is greater than the cost of capital, accept the project.
If the IRR is less than the cost of capital, reject the project.
Steps:
Draw a timeline for the cash flows
𝐼𝑜𝑢𝑡 = R500 000
𝐶1 =75 000 𝐶2 = 190 000 𝐶3 =40 000 𝐶4 =150 000 𝐶5 =180 000
75 000 190 000 40 000 150 000 180 000
Now f (i) = + + + + - 500 000
(1+𝑖) (1+𝑖)2 (1+𝑖)3 (1+𝑖)4 (1+𝑖)5
We must determine i such that f (i) = 0.
Use calculator to solve i
We find that the internal rate of return for the investment is 7.78%. Reject proposal
[Option 1]
2
, DSC1630 ASSIGNMENT 04 2022 UNIQUE NUMBER 632596
Question 2
The net present value (NPV) is approximately
[1] R135 000.
[2] −R135 000.
[3] −R30 523.
[4] R74 500.
Notes; NPV definition: The net present value (NPV) of an investment proposal is the present value of all
future cash inflows (𝑃𝑉𝑖𝑛 ) less the investment outlay (𝐼𝑜𝑢𝑡 )
If the NPV is positive (greater than zero), the proposal may be regarded as acceptable. If it is negative
(smaller than zero), it is not. And if it is zero, the investor will be indifferent.
NPV = 𝑃𝑉𝑖𝑛 - 𝐼𝑜𝑢𝑡
𝐶1 𝐶2 𝐶3 𝐶4 𝐶5
NPV = + + + + - 𝐼𝑜𝑢𝑡
1+𝐾 (1+𝐾)2 (1+𝐾)3 (1+𝐾)4 (1+𝐾)5
75000 190000 40000 150000 180000
= + + + + – 500000
1.1 (1.1)2 (1.1)3 (1.1)4 (1.1)5
= 68181.82 + 157024.79 + 30052.59+ 102452.02+ 111765.84 -500000
= 469477.06 -500000
= - 30 522.94
= -R30 523
If you use the calculator it agrees with this same amount. Therefore reject proposal
[Option 3]
3
