Corporate Finance, Module 2: "How to Calculate Present Values"

Homework Assignment

The homework exercises are modeled after the practice problems for this module. The cover the basic formulas needed for net present value calculations. The final exam tests the financial theory, not the background mathematics, but these methods are needed to solve the financial problems.

Exercise 2.1: Compounding Intervals

What is the value of $6,000 after 6 years invested at 3% a quarter?

Exercise 2.2: Doubling Investments

How long will it take a dollar to double if it is invested at

5%

12%

Use logarithms to compute the answer: $2 = $1 × (1 + r)^t A ln 2 = t × ln (1 + r).

 

Exercise 2.3: Net Present Value

What is the net present value of an investment of $2,500 that produces income of $670 a year for 5 years at a discount rate of 10% per annum? Show the solution with discount factors and with the annuity formula.

 

Exercise 2.4: Net Present Value

What is the net present value of an investment costing $2,000 that produces cash flows of $700 in year 1, $700 in year 2, and $900 in year 3 if the discount rate is 10%?

 

Exercise 2.5: Savings and Consumption

A worker now has $10,000 and expects to save an $5,000 next year and then pay $4,000 in 2 years’ time and $3,000 in 3 years’ time for a new car. How much of the present savings can the worker spend now on a dining room set if savings earn 7%?

 

Exercise 2.6: Perpetuity

A lottery winner receives $750 in 1 year’s time and annually thereafter in perpetuity. What is the value of this perpetuity at an interest rate of 10%?

 

Exercise 2.7: Delayed Perpetuity

How much is the previous perpetuity worth if it begins in 10 years time instead of in 1?

 

Exercise 2.8: Growing Perpetuity

If the lottery winner receives $750 in 1 year’s time and this amount increases 5% per annum, what is the present value of this growing income stream at a 10% interest rate?

In question 2.5, it says the worker expects to save $5000 next year.  Does that mean to say he will earn $5000 next year? The word "save" is confusing, as if he is saving part of the $10,000 he has now.

The word "save" is used by Brealey and Myers. They mean earn in excess of expenses. If a person earns $25,000 and spends $20,000 on food and rent, he or she has $5,000 to spend on other matters.  You are right; it is not the best term.

Is it 3% a quarter, or 3% annually compounded quarterly?  Just want to make sure the wording is clear.

[NEAS: 3% a quarter, or 12% a year compounded quarterly.]

In exercise 2.3 you have a discount rate of 10%.  Is that the same as the discount fator that is shown in the book, like 10%=1-v, so v = .9?  or is 10% = r, the interest rate?

It's the actual discount rate.

If it's the actual discount rate, we should be getting an interest rate using d/(1-d) correct? But this gives negative present values, so no one would actually invest in these cash flows.

W

I have trouble finding the correct answers in this forum. Can anyone confirm if you get the same answers like mine? Thanks!

Ex 2.1
12,197

Ex 2.2
(A) 14.2 Years
(B) 6.12 Years

Ex 2.3
NPV = 40

Ex 2.4
NPV = -109

Ex 2.5
8,730

Ex 2.6
7,500

Ex 2.7
2,892

Ex 2.8
15,000

Gordon

Ex 2.7
2,892

Gordon, remember that a payment at the end of 10 years is only 9 years after a payment at the end of 1 year.

um.. sounds like the question is not clear..

so the lottery winner will get 750 at the end of year one..
and the second payment in year 10?!

as i read the question, the winner will get his/her first payment at the end of year 10...
so we should calculate the value of the perpetuity at year 10...
then discount it back into year 1...

did i misunderstand the question?

[NEAS: The perpetuity begins in year 10, so discount back to beginning date.]

Gordon