Time Value of Money (BL- 06)

Part A
1. Future Value
Calculate the value 5 years hence of a deposit of ₹1,000 made today if the interest rate
is (a) 8 percent, (b) 10 percent, (c) 12 percent, and (d) 15 percent.

2. Rule of 72
If you deposit ₹5,000 today at 12 percent rate of interest in how many years (roughly)
will this amount grow to ₹1,60,000? Work out this problem using the rule of 72—do
not use tables.

3. Future Value
You can save ₹2,000 a year for 5 years, and ₹3,000 a year for 10 years thereafter. What
will these savings cumulate to at the end of 15 years, if the rate of interest is 10 percent?

4. Annual Savings
Mr. Vinay plans to send his son for studies abroad after 10 years. He expects the cost
of these studies to be ₹1,000,000. How much should he save annually towards a sum
of ₹1,000,000 at the end of 10 years, if the interest rate is 12 percent?

5. Interest Rate
A finance company advertises that it will pay a sum of ₹10,000 at the end of 6 years to
investors who deposit annually ₹1,000. What interest rate is implicit in this offer?

6. Present Value
What is the present value of a stream of ₹2,000 at 10 percent for 5 years?

7. Retirement Plan
On retirement, Mr. Jingo is given a choice between two alternatives: (a) an annual
pension of ₹10,000 as long as he lives, and (b) a lump sum amount of ₹50,000. If Mr.
Jingo expects to live for 15 years and the interest rate is 15 percent, which option is
more attractive?

8. Annual Withdrawal
Mr. X deposits ₹1,00,000 in a bank which pays 10 percent interest. How much can he
withdraw annually for a period of 30 years. Assume that at the end of 30 years the
amount deposited will dwindle down to zero.

9. Present Value
What is the present value of an income stream which provides ₹1,000 at the end of year
one, ₹2,500 at the end of year two, and ₹5,000 during each of the years 3 through 10,
if the discount rate is 12 percent?
10. Present Value
What is the present value of an income stream of ₹2,000 a year for the first five years
and ₹3,000 a year forever thereafter, if the discount rate is 10 percent?

11. Interest Rate

Suppose someone offers you the following financial contract. If you deposit ₹20,000
with him he promises to pay ₹4,000 annually for 10 years. What is the interest rate?

12. Present Value

What is the present value of the following cash flow streams?

Year 1 2 3 4 5 6 7 8 9 10
A 100 200 300 400 500 600 700 800 900 1000
B 1000 900 800 700 600 500 400 300 200 100
C 500 500 500 500 500 500 500 500 500 500

The discount rate is 12 percent.

13. Future Value

Suppose you deposit ₹10,000 with an investment company which pays 16 percent
interest with quarterly compounding. How much will this deposit grow to in 5 years?

14. Interest Rate

Mr. Prakash buys a motorcycle with a bank loan of ₹60,000. An installment of ₹3,000
is payable to the bank for each of 24 months towards the repayment of loan with interest.
What interest rate is being charged?
15. Loan Amortisation
Phoenix Company borrows ₹500,000 at an interest rate of 14 percent. The loan is to be
repaid in 4 equal annual instalments payable at the end of the next 4 years. Prepare an
amortisation schedule.
16. Present Value
As a winner of a competition, you can choose one of the following prizes:
a. ₹500,000 now
b. ₹1,000,000 at the end of 6 years
c. ₹60,000 a year forever
d. ₹100,000 per year for 10 years
e. ₹35,000 next year and rising thereafter by 5 percent per year forever.
If the interest rate is 10 percent, which prize has the highest present value?
17. Present Value of a Decreasing Annuity
Pipe India owns an oil pipeline which will generate ₹12 crore of cash income in the
coming year. It has a very long life with virtually negligible operating costs. The volume
 of oil shipped, however, will decline over time and, hence, cash flows will decrease by
3 percent per year. The discount rate is 12 percent.

a. If the pipeline is used forever, what is the present value of its cash flows?
b. If the pipeline is scrapped after 25 years, what is the present value of its cash flows?

Part B

1. Anand, an investment banker, is evaluating a proposal where Swiggy Instamart seeks

₹50 lakhs in funding to expand into 20 new tier-2 cities. In return, Swiggy promises to
pay him ₹15 lakhs per year for the next 5 years.
Arjun wants to assess whether this investment is worthwhile if his required rate of
return is 12% per annum.

2. Your grandfather bought a piece of land 75 years ago and built a small warehouse.
Currently, according to your grandfather’s will, the warehouse has been endowed to
you. You intend to lease it to tenants and receive lease income forever. You have two
choices on leasing the place.
Client A would like to lease the place by paying the first payment of ₹ 150000 at the
end of the year. In this contract, the payments increase at a rate of 5% for 10 years at
which point the agreement terminates.
Client B, on the other hand does not prefer to pay an increasing lease and prefers a fixed
lease per year (end of year). Suppose, you choose client B as your choice, how much
should you charge the client per year so that you’re indifferent between the two clients?
Assume interest rate of 12%.

3. You have just turned 30. Your parents are urging you to buy a house by taking a loan
of ₹ 5,000,000 at 9% APR, 15 years repayment with monthly EMI (payments at end of
month). Unfortunately, you listened to your CF professor yesterday who suggested that
investing the equivalent of EMI is better than buying a house.
Suppose you find an investment that yields an EAR of 15% and you think instead of
paying EMI, you can invest that money in this investment and later on use the
compounded returns to buy a house with cash. What must be the price of a house 15
years from now that makes you indifferent between the two choices?

4. You are evaluating an income-generating property. Net rent is received at the end of
each year. The first year’s rent is expected to be $8,500, and rent is expected to increase
7 percent each year. What is the present value of the estimated income stream over the
first five years if the discount rate is 12 percent?
 Part C

Textbook Mini Case

Ben Bates graduated from college six years ago with a finance undergraduate degree.
Although he is satisfied with his current job, his goal is to become an investment banker.
He feels that an MBA degree would allow him to achieve this goal. After examining
schools, he has narrowed his choice to either Wilton University or Mount Perry College.
Although internships are encouraged by both schools, to get class credit for the
internship, no salary can be paid. Other than internships, neither school will allow its
students to work while enrolled in its MBA program.
Ben currently works at the money management firm of Dewey and Louis. His annual
salary at the firm is $69,000 per year, and his salary is expected to increase at 3 percent
per year until retirement. He is currently 28 years old and expects to work for 40 more
years. His current job includes a fully paid health insurance plan, and his current
average tax rate is 26 percent. Ben has a savings account with enough money to cover
the entire cost of his MBA program.
The Ritter College of Business at Wilton University is one of the top MBA programs
in the country. The MBA degree requires two years of full-time enrollment at the
university. The annual tuition is $75,000, payable at the beginning of each school year.
Books and other supplies are estimated to cost $3,600 per year. Ben expects that after
graduation from Wilton, he will receive a job offer for about $115,000 per year, with a
$20,000 signing bonus. The salary at this job will increase at 4 percent per year. Because
of the higher salary, his average income tax rate will increase to 31 percent.
The Bradley School of Business at Mount Perry College began its MBA program 16
years ago. The Bradley School is smaller and less well known than the Ritter College.
Bradley offers an accelerated, one-year program, with a tuition cost of $90,000 to be
paid upon matriculation. Books and other supplies for the program are expected to cost
$5,400. Ben thinks that he will receive an offer of $96,000 per year upon graduation,
with an $18,000 signing bonus. The salary at this job will increase at 3.5 percent per
year. His average tax rate at this level of income will be 29 percent.
Both schools offer a health insurance plan that will cost $3,500 per year, payable at the
beginning of the year. Ben also estimates that room and board expenses will cost $2,500
more per year at both schools than his current expenses, payable at the beginning of
each year. The appropriate discount rate is 4.7 percent.

Questions:
1. How does Ben’s age affect his decision to get an MBA?
2. What other, perhaps nonquantifiable, factors affect Ben’s decision to get an MBA?
3. Assuming all salaries are paid at the end of each year, what is the best option for Ben—
from a strictly financial standpoint?
4. Ben believes that the appropriate analysis is to calculate the future value of each option.
How would you evaluate this statement?
5. What initial salary would Ben need to receive to make him indifferent between
attending Wilton University and staying in his current position?
6. Suppose, instead of being able to pay cash for his MBA, Ben must borrow the money.
The current borrowing rate is 4.3 percent. How would this affect his decision?
 Answers
Part A
Q1 1,469 1,611 1,762 Q7 58,474 (choice A) Q13 21,911
2,011
Q2 30 Q8 10,608 Q14 1.51%
Q3 79,482 Q9 22,687 Q15 EMI= 1,71,602
Q4 56,984 Q10 26,209 Q16 Choice e
Q5 17.46% Q11 15.10% Q17 a. 80,00,00,000; b.
77,80,24,803
Q6 7,582 Q12 2,590.4; 3,624.8; 2,825.1 Q18

Part B
Q1 407164 is the NPV. Accept Q7 Q13
Q2 ₹1,80,349.21 Q8 Q14
Q3 3,08,46,470 Q9 Q15
Q4 $34,706.26 Q10 Q16
Q5 Q11 Q17
Q6 Q12 Q18

Part C
Present value of
salary $14,43,065.93
PV of attending
Wilton $21,74,034.77
PV of attending Mt.
Perry $18,75,203.83
Current job PV minus
bonus after Wilton
costs $15,95,879.38
Aftertax beginning
salary $54,422.56;
Pretax beginning
salary $78,873.27