Kitty, a rising pop music artist is negotiating with EBI Music Company for the terms of her new 3-year contract. EBI offers two alternatives for her remuneration:
(a) An upfront payment of $6,000,000; or
(b) Payment of $2,200,000 at the end of each year for the next three years.
Suppose the appropriate interest rate is 5%, advise Kitty which package to take.
Topic C07: Time Value of Money Student Worksheet p.6
BAFS Learning and Teaching Example Updated in 2022
Problem 6: Future Value of an Annuity
Daniel plans to take a backpack trip to Europe after his university graduation, and he is expected to save up $20,000 at the end of each year in the coming 3 years. If he can earn 3.5% interest per year from his savings, how much would he have at the end of the third year?
Topic C07: Time Value of Money Student Worksheet p.7
BAFS Learning and Teaching Example Updated in 2022
Problem 7: Present Value of Uneven Cash Flows
Using a discount rate of 7%, what is the total present value of the following series of cash flows?
End of first year $12,000 End of second year $22,000 End of third year $ 5,000
Topic C07: Time Value of Money Student Worksheet p.8
BAFS Learning and Teaching Example Updated in 2022
Problem 8: Future Value of Uneven Cash Flows
Based on an interest rate of 7%, what is the future value of the following series of cash flows?
End of first year $12,000 End of second year $22,000 End of third year $ 5,000
Topic C07: Time Value of Money Student Worksheet p.9
BAFS Learning and Teaching Example Updated in 2022
Problem 9: NRR Vs ERR
Ken received a bonus worth $100,000. He plans to deposit the money into a savings account for 2 years. Which of the following savings plans should he choose and how much will he obtain at the maturity date?
Plan I Plan II
Interest rate 5.5% 6.5%
Frequency of interest compounding
Half-yearly Yearly
Topic C07: Time Value of Money Student Worksheet p.10
BAFS Learning and Teaching Example Updated in 2022
Topic C07: Time Value of Money Student Worksheet p.1
BAFS Learning and Teaching Example Updated in 2022
BAFS Compulsory Part - Basics of Personal Financial Management
Topic C07: Fundamentals of Financial Management - Time Value of Money
Problem Solving
Problem 1: Future Value of a Single Cash Flow
Your mother has bought $4,500 Australian dollars and placed it in the bank on a fixed deposit term of 1 year. If the deposit interest rate is 5.19% per year, how much will she have at the maturity of the deposit?
Solution:
At the maturity of the deposit, your mother will have:
FV = PV × (1 + r)
= A$4,500 × (1 + 0.0519) = A$4,733.55
Topic C07: Time Value of Money Student Worksheet p.2
BAFS Learning and Teaching Example Updated in 2022
Problem 2: Future Value of a Single Cash Flow Using Compound Interest
An investment product promises to pay an 8% return for each year, compounded annually. How much will an initial investment of
$100,000 become at the end of the 3rd year?
Solution:
FV = PV × (1 + r)n
= $100,000 × (1 + 0.08)3
= $125,971.20
Problem 3: Future Value of a Single Cash Flow Using Compounding
You have made a 3-year fixed New Zealand dollar deposit today.
The principal amount is NZ$10,000 and interest rate is 6.75%, compounded yearly. How much would you get back at the maturity of your deposit?
Solution:
FV = PV × (1 + r)n
= NZ$10,000 × (1 + 0.0675)3 = NZ$12,164.76
Topic C07: Time Value of Money Student Worksheet p.3
BAFS Learning and Teaching Example Updated in 2022
Problem 4a: Present Value of a Single Cash Flow (multi-year periods)
How much would you be willing to lend to Thomson with a current interest rate of 3%, if he promises to pay you $1,000 in 1 year time?
What if Thomson pays you 3 years later?
Solution:
For 1 year:
PV = FV / (1 + r)
= $1,000 / 1.03
= $970.87
For 3 years:
PV = FV / (1 + r)n
= $1,000 / 1.033
= $915.14
Problem 4b: Present Value of a Single Cash Flow (multi-compounding periods in a year)
Jason wants to renovate his house at $200,000 a year later. If the interest rate is 6% per annum, compounded semi-annually, how much does he need to deposit into his bank account now to save up for the renovation work?
Solution:
The amount to be deposited into bank now:
PV = FV / (1 + r)n
= $200,000 / (1.03)2
= $188,501
Topic C07: Time Value of Money Student Worksheet p.4
BAFS Learning and Teaching Example Updated in 2022
Extended Learning (Lesson 2)
Challenging Problem: Rule of 72
Today is Jacky’s 30th birthday and he is working on a retirement plan. Currently, he has a saving of $100,000 and plan to invest the money in a mutual fund that is expected to have an annual rate of return of 12%. By means of the Rule of 72, estimate:
(a) How long will it take for the investment to double?
(b) How much would the investment be worth when Jacky is 60 years old?
Solution:
(a) By the Rule of 72, it takes about 6 years (i.e. 72/12) for the investment to double.
(b) The investment period equals 60 – 30 = 30 years, and given the investment will double every 6 years, the investment will double 30 / 6 = 5 times. So $100,000 will grow to $100,000
× 25 = $3,200,000.
Topic C07: Time Value of Money Student Worksheet p.5
BAFS Learning and Teaching Example Updated in 2022
Problem 5: Future Value of an Annuity
Kitty, a rising pop music artist is negotiating with EBI Music Company for the terms of her new 3-year contract. EBI offers two alternatives for her remuneration:
(a) An upfront payment of $6,000,000; or
(b) Payment of $2,200,000 at the end of each year for the next three years.
Suppose the appropriate interest rate is 5%, advise Kitty which package to take.
Solution:
PV of first $2,200,000 = $2,200,000 / 1.05
= $2,095,238.10 PV of second $2,200,000 = $2,200,000 / 1.052
= $1,995,464.85 PV of third $2,200,000 = $2,200,000 / 1.053
= $1,900,442.72 PV of annuity = Total PVs
= $5,991,145.67 which is less than $6,000,000.
Thus, Kitty is better off to be paid $6,000,000 upfront.
Topic C07: Time Value of Money Student Worksheet p.6
BAFS Learning and Teaching Example Updated in 2022
Problem 6: Future Value of an Annuity
Daniel plans to take a backpack trip to Europe after his university graduation, and he is expected to save up $20,000 at the end of each year in the coming 3 years. If he can earn 3.5% interest per year from his savings, how much would he have at the end of the third year?
Solution:
Total FVs:
= $20,000 × (1+0.035)2
+ $20,000 × (1+0.035) + $20,000 = $21,424.5 + $20,700 + $20,000 = $62,124.5
Topic C07: Time Value of Money Student Worksheet p.7
BAFS Learning and Teaching Example Updated in 2022
Problem 7: Present Value of Uneven Cash Flows
Using a discount rate of 7%, what is the total present value of the following series of cash flows?
End of first year $12,000 End of second year $22,000 End of third year $ 5,000
Solution:
PV of $12,000 in the first year
= $12,000 / 1.07
= $11,214.95
PV of $22,000 in the second year
= $22,000 / 1.072
= $19,215.65
PV of $5,000 in the third year
= $5,000 / 1.073
= $4,081.49 Total PVs = $34,512.09
Topic C07: Time Value of Money Student Worksheet p.8
BAFS Learning and Teaching Example Updated in 2022
Problem 8: Future Value of Uneven Cash Flows
Based on an interest rate of 7%, what is the future value of the following series of cash flows?
End of first year $12,000 End of second year $22,000 End of third year $ 5,000
Solution:
FV of $12,000 in Year 1
= $12,000 × 1.072
= $13,738.80 FV of $22,000 in Year 2
= $22,000 × 1.07
= $23,540 FV of $5,000 in Year 3
= $5,000
Total FVs = $42,278.80
Topic C07: Time Value of Money Student Worksheet p.9
BAFS Learning and Teaching Example Updated in 2022
Problem 9: NRR Vs ERR
Ken received a bonus worth $100,000. He plans to deposit the money into a savings account for 2 years. Which of the following savings plans should he choose and how much will he obtain at the maturity date?
Plan I Plan II
Interest rate 5.5% 6.5%
Frequency of interest compounding
Half-yearly Yearly
Solution:
ERR of each plan are as follows:
ERR of Plan I ERR of Plan II
(1+0.055/2) 2 -1
= 5.6%
(1+0.065) 1 -1
= 6.5%
Plan II offers a higher return.
FV of Plan II:
$100,000 x (1+6.5%) 2
= $113,422.5