# Investment Analysis LEC 4 by AhsanTareen

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Lecture 4

Complications in NPV
Investment Analysis

Complication 1
Inflation
How does inflation affect DCF analysis?

CF1 CF2 CF3 CF4 CF5
NPV = + + + + +…
(1+r) (1+r)2 (1+r)3 (1+r)4 (1+r)5

Discounting Rule

Treat inflation consistently: Discount real cash flows at the real
interest rate and nominal cash flows at the nominal interest rate.
Investment Analysis

Complication 1 (cont‟d …)
Terminologies
Cash flows
Nominal = Actual Cash Flows
Real = Cash Flows expressed in today‟s purchasing power

Real CFt = Nominal CFt / (1 + Interest Rate)t

Discount Rates
Nominal = Actual Interest Rate
Real = Interest Rate adjusted for Inflation

1 + Real Interest Rate = (1 + Nominal Interest Rate) / (1 + Inflation Rate)

Real Interest Rate = [(1 + Nominal Interest Rate) / (1 + Inflation Rate)] - 1
Investment Analysis

Example

This year you earned \$100,000. You expect
real terms, for the remaining 20 years of
your career. Interest rate is currently 5% and
inflation rate is 2%. What is the present
Investment Analysis

Complication 2

Compounding Frequency

On many investments or loans, interest is often charged or credited more
than once a year.

Examples
Bank Accounts – Daily
Mortgages and Leases – Monthly
Bonds – Semiannually

Implication
Effective Annual Rate (EAR) can be much different that the stated Annual
Percentage Rate (APR).
Investment Analysis

Compounding

- Consider investing \$100 at the annual interest rate 10%. How much will your
investment value in 3 years?
> After 1 year you will have:
\$100 x 1.1 = \$110
> After 2 years you will have:
\$100 x 1.12 = \$121
> After 3 years you will have:
\$100 x 1.13 = \$133.1
- This is different from \$100 + \$30 = \$130
- Have to account for interest on interest.

- More generally, investing C dollars at the annual interest rate r gives,
C ( 1 + r )t dollars after t years.
Investment Analysis

APRs & EARs

Habib Bank quotes you a rate of 7% for your home mortgage. The
mortgage involves monthly payments.

o   7% is not the “true” annual rate, it is only used to derive the monthly rate by:

x = 7% / 12 = 0.583%

o   The “true” annual rate is:

(1 + x)12 – 1 = 7.23%

o   7% is the Annual Percentage Rate (APR). It is the quoted rate.

o   7.23% is the Effective Annual Rate (EAR). It is the true rate.
Investment Analysis

APRs & EARs : Compounding Frequencies

Example: Suppose your bank offers a 1-year CD with a 5% APR, what is the
EAR with;

•   Annual Compounding? 1.05
•   Semiannual Compounding? (1+ 5%/2 )2=1.050625
•   Quarterly Compounding? (1+ 5%/4 )4=1.050945
•   Monthly Compounding? (1+ 5%/12 )12=1.051161
•   Daily Compounding? (1+ 5%/360 )360=1.01267
•   Continuous Compounding? Lim (1+ 5%/T )T=…
T∞
General Formula: with T compounding periods in a year
APR
EAR = ( 1 + ) T - 1
T
Investment Analysis

APRs & EARs (cont’d …)

Example

Car Loan
„Finance charge on an unpaid balance, computed daily, is at the rate of 6.75% per year.

If you borrow \$10,000 to be repaid in one year. How much would you owe in a year?

Daily Interest Rate = 6.75 / 365 = 0.0185%

Day 1: balance = 10,000 x 1.00185 = 10,001.85
Day 2: balance = 10,000 x (1.00185)2 = 10,003.70
……….. …………………………………………………………………
Day 4: balance = 10,000 x (1.00185)360 = 10,698.50

EAR = 6.985%
Investment Analysis

Complication 2 (cont‟d …)

Discounting Rule
In applications, interest is compounded at the same frequency as
payments.

If, so just divide the APR by number of compounding intervals.

Bonds
Make semiannual payments, interest compounded semiannually,
discount semiannual cash flows by APR / 2.

Mortgages
Make monthly payments, interest compounded monthly, discount
monthly cash flows by APR / 12.
Investment Analysis

Complication 3

Currencies
How foreign currency cash flows are discounted?

CF1 CF2 CF3 CF4
PV = CF0 + + + + +…
(1+r) (1+r)2 (1+r)3 (1+r)4

Discounting Rule
Discount each currency at its own interest rate: discount \$ at the U.S
interest rate, discount € at the european interest rate.

This gives of PV of each cash flow stream in its own currency.

Convert to domestic currency at the current exchange rate.
Investment Analysis

Currencies (cont’d …)

Logic
You have \$1 now. How many Euros can you convert this
into in 1 year? The current exchange rate is 1.6 \$/€ and
the European interest rate is 5%.

Today: \$1 = €0.625
1 year: €0.625 x 1.05 = €0.6563

Implication: \$1 today is worth 0.6563 pounds in one
year.
Investment Analysis

Example

Your firm just signed a contract to deliver 2,000 batteries in
each of the next 2 years to a customer in Japan, at a per unit
price of ¥800. It also signed a contract to deliver 1,500
batteries in each of the next 2 years to a customer in Britain,
at a per unit price of £6.2. Payment is certain and occurs at
the end of the year.

The British interest rate r£ = 5% and the Japanese interest
rate is r¥ = 3.5%. The exchange rates are 118¥/\$ and 1.6\$/£.

What is the value of each contract?

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