Fundamentals of Corporate Finance

Chapter 5

Discounted Cash Flow Valuation

Overview of Lecture

Corporate Finance in the News

Insert a current news story here to frame the material you will cover in the lecture.

Future Value with Multiple Cash Flows

Suppose you deposit €100 today in an account paying 8 per cent. In one year, you will deposit another €100. How much will you have in two years?

Future Value with Multiple Cash Flows

Consider the future value of €2,000 invested at the end of each of the next five years. The current balance is zero, and the rate is 10 per cent.

Future Value with Multiple Cash Flows

Consider the future value of €2,000 invested at the end of each of the next five years. The current balance is zero, and the rate is 10 per cent.

Example 5.1Saving Up Once Again

Example 5.1Saving Up Once Again

Present Value with Multiple Cash Flows

Present Value with Multiple Cash Flows

Example 5.2How Much is it Worth?

Example 5.2How Much is it Worth?

Example 5.3How Much is it Worth Part 2?

Example 5.3How Much is it Worth Part 2?

Spreadsheet Strategies

Now that the students have got a good idea how to do PV and FV calculations, spreadsheets should be covered now to illustrate how they can be used for these types of problems.

Cash Flow Timing

Valuing Level Cash Flows: Annuities and Perpetuities

Present Value for Annuity Cash Flows

Present Value for Annuity Cash Flows

PV of an Annuity Formula

1 Present value factorAnnuity present value =

1 [1 / (1 ) ]

1 1

(1 )

t

t

Crr

Cr

Cr r r

The present value of an annuity of £C (or any other currency) per period for t periods when the rate of return or interest rate is r is given by:

Example 5.4How Much Can You Afford?

Example 5.4How Much Can You Afford?

The loan payments are in ordinary annuity form, so the annuity present value factor is: 

Annuity PV factor = (1 Present value factor)/r = [1 (1/1.0148)]/.01 = (1 .6203)/.01 = 37.9740

 With this factor, we can calculate the present value of the 48 payments of €632 each as: 

Present value = €632 37.9740 = €24,000

Table 5.1Annuity Present Value Interest Factors

Spreadsheet Strategies

Show how to use a spreadsheet to calculate the present value of an annuity

Example 5.5Finding the Number of Payments

Example 5.5Finding the Number of Payments

Future Value of Annuities

Annuity FV factor = (Future value factor 1) /[(1 + ) 1] /(1 ) 1

t

t

rr rr

r r

(1 ) 1FV of Annuity

trC

r r

Annuities Due

Perpetuities

Perpetuities

Preference Shares

Example 5.6Preference Shares

Example 5.6Preference Shares

Growing Annuities

11

1Growing annuity present value

tgrC

r g

Growing Perpetuities

1Growing perpetuity present value

CC

r g r g

Comparing Rates

Comparing Rates

Comparing Rates

12

12

EAR = [1 + (Quoted rate/ )] 1= [1 + (.12/12)] 1= 1.01 1= 1.126825 1= 12.6825%

mm

Example 5.7What’s the EAR?

Example 5.7What’s the EAR?

The bank is effectively offering 12%/4 = 3% every quarter. If you invest £100 for four periods at 3 per cent per period, the future value is:

4

£=£=

Future value = £100 1.03100 1.1255112.55

The EAR is 12.55 per cent: £100 (1 + .1255) = £112.55.

Example 5.7What’s the EAR?

Example 5.8Quoting a Rate

Example 5.8Quoting a Rate

12

12

EAR = [1 + (Quoted rate/ )] 1.18 = [1 + ( /12)] 1

1.18 = [1 + ( /12)]

mmqq

The Annual Percentage Rate

The Annual Percentage Rate

Example 4.14: APR

The sale price of a car is £30,000.

The quoted rate is “a simple annual interest rate of 12 percent on the original borrowed amount over three years, payable in 36 monthly installments.”

The finance company also charges an administration fee of £250. What does this mean?

The lender will charge 12 percent interest on the original loan of £30,000 every year for three years.

Each year, the interest charge will be (12% of £30,000) £3,600 making a total interest payment of £10,800 over three years.

Example 4.14: APR

Example 4.14: APR

What is the APR of this loan?

This gives an Annual Percentage Rate (APR) of 24.13%!

The lender must also state the total amount paid at the end of the loan, which, in this case, is £41,049.88 and the total charge for credit is £11,049.88 (£41,049.88 - £30,000).

1 2 36

12 12 12

£1,133.33 £1,133.33 £1,133.33£30,000 £250

(1 APR) (1+APR) (1+ APR)

L

Continuous Compounding

Continuous Compounding Formula

Loan Types and Loan Amortization

Example 5.10Treasury Bills

Example 5.10Treasury Bills

Example 5.10Treasury Bills

Example 5.10Treasury Bills

Example 5.10Treasury Bills

Spreadsheet Strategies

You should now take the students through some examples on the spreadsheet.

Activities for this Lecture

Thank You