ENGINEERING

ECONOMY
IV. DECISIONS UNDER CERTAINTY
DISCOUNT AND INFLATION

ENGR. SHELAH GRACE HEBRA

Discount
Discount on a negotiable paper is the difference between the present
worth (the amount received for the paper in cash) and the worth of
the paper at some time in the future ( the face value of the paper or
principal). Discount is interest paid in advanced
Discount = Future Worth - Present Worth
𝐷𝑖𝑠𝑐𝑜𝑢𝑛𝑡 The rate of discount is
𝑑= the discount on one
𝐹𝑢𝑡𝑢𝑟𝑒 𝑊𝑜𝑟𝑡ℎ unit of principal for
𝑑 one unit of time
𝑖=
𝑑 = 1 − 1 + 𝑖 −1 1−𝑑

Where: d= rate of discount for the period involved

i= rate of interest for the same period
Discount
Sample problem:

A man borrowed P5,000 from a bank and agreed to pay the loan at
the end of 9 months. The bank discounted the loan and gave him
P4,000 in cash. (a) What was the rate of discount? (b) what was the
rate of interest? (c) What was the rate of interest for one year?
We are all very aware that P20 now does not purchase
the same amount of P20 did in 1995 or 1996 and
purchases significantly less than in 1980. Why?
 INFLATION

In the last few years of 20th century and the beginning of the 21st
century, inflation has not been a major concern in the U.S. or most
industrialized nations. But the inflation rate is sensitive to real, as well
as perceived, factors of the economy.
Factors such as the cost of energy, interest rates, availability and cost
of skilled people, scarcity of materials, political stability, and other,
less tangible factors have short-term and long-term impacts on the
inflation rate
 INFLATION
Inflation is an increase in the amount of money necessary to obtain
the same amount of product or service before the inflated price was
present.

Inflation occurs because the value of the currency has changed- it

has gone down in value. The value of money has decreased, and as a
result, it takes more dollars for the same amount of goods or services.
This is a sign of inflation.

Deflation is the opposite of inflation in that when deflation is present,

the purchasing power of the monetary unit is greater in the future
than in the present.
 INFLATION

𝑃𝑒𝑠𝑜 𝑖𝑛 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡2
𝑃𝑒𝑠𝑜 𝑖𝑛 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡1 =
𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑡1 𝑎𝑛𝑑 𝑡2

′
𝑓𝑢𝑡𝑢𝑟𝑒 𝑝𝑒𝑠𝑜
𝑡𝑜𝑑𝑎𝑦 𝑠 𝑝𝑒𝑠𝑜 =
(1 + 𝑓)𝑛

𝑓𝑢𝑡𝑢𝑟𝑒 𝑝𝑒𝑠𝑜 = 𝑡𝑜𝑑𝑎𝑦 ′ 𝑠 𝑝𝑒𝑠𝑜 (1 + 𝑓)𝑛

 THREE DIFFERENT RATES OF INFLATION

REAL OR INFLATION-FREE INTEREST RATE, 𝑖 – the rate at

which interest is earned when the effect of changes in the
value of currency (inflation) have been removed.

INLFATION-ADJUSTED INTEREST RATE 𝑖𝑓 - the interest rate

that has been adjusted to take inflation into account
(market interest rate)

INFLATION RATE, 𝑓- a measure of the rate of change in the

value of currency.
 INFLATION
PW CALCULATIONS ADJUSTED FOR INFLATION

1
𝑃=𝐹
(1 + 𝑖𝑓 )𝑛
Where:

𝑖𝑓 = 𝑖 + 𝑓 + 𝑖𝑓

𝑖= real interest rate

𝑓= inflation rate
 INFLATION
PW CALCULATIONS ADJUSTED FOR INFLATION

For a real interest rate of 10% per year and an inflation rate of
4% per year,

𝑖𝑓 = 𝑖 + 𝑓 + 𝑖𝑓
𝑖𝑓 = 0.10 + 0.04 + 0.10 0.04 = 0.144
 INFLATION
PW CALCULATIONS ADJUSTED FOR INFLATION

Example
A former student of an engineering department wishes to donate to the
department’s scholarship fund. Three options are available:
Plan A: $60,000 now
Plan B: $15,000 per year for 8 years beginning 1 year from now.
Plan C: $50,000 three years from now and another $80,000 five years from now.

From the department’s perspective it wants to select the plan that maximizes the
buying of the dollars received. The department head asked the engineering
professor evaluating the plans to account for inflation in the calculations. If the
donation earns a real 10% per year and the inflation rate is expected to average
3% per year, which plan should be accepted?
 INFLATION
PW CALCULATIONS ADJUSTED FOR INFLATION
A self-employed chemical engineer is on contract with Dow Chemical, currently
working in a relatively high-inflation country. She wishes to calculate a project’s
PW with estimated costs of $35,000 now and $7,000 per year for 5 years
beginning 2 year from now wit increases of 12% per year thereafter for the next
8 years. Use a real interest rate of 15% per year to make the calculations (a)
without an adjustment for inflation (b) considering inflation at a rate of 11% per
year.
 INFLATION
FW CALCULATIONS ADJUSTED FOR INFLATION

In future worth calculations, a future amount F can have any one of

four different interpretations:
Case 1. The actual amount of money that will be accumulated at
time n.
Case 2. The purchasing power of the actual amount accumulated
at time n, but stated in today’s (constant-value) dollars.
Case 3: The number of future dollars required at time n to maintain
the same purchasing power as a dollar today; that is, inflations is
considered, but interest is not
Case 4: the number of dollars required at time n to maintain
purchasing power and earn a stated real interest rate
 INFLATION FW CALCULATIONS ADJUSTED FOR INFLATION

Case 1: Actual Amount Accumulated

𝐹 = 𝑃(1 + 𝑖𝑓 )𝑛

Ex. When we are quoted a market rate of 10%, the inflation rate is
included. Over a 7 year period, $1000 will accumulate to
𝐹 = 1000(1 + 0.10)7
𝐹 = $1948.72
 INFLATION FW CALCULATIONS ADJUSTED FOR INFLATION

Case 2: Constant-Value with purchasing power

𝑃(1 + 𝑖𝑓 )𝑛
𝐹=
(1 + 𝑓)𝑛
The purchasing power of future dollars is determined by first
using the market rate 𝑖𝑓 to calculate F and then deflating the
future amount through division by (1 + 𝑓)𝑛

The percentage loss in purchasing power is a measure of how

much less.
 INFLATION FW CALCULATIONS ADJUSTED FOR INFLATION

Case 2: Constant-Value with purchasing power

𝑃(1 + 𝑖𝑓 )𝑛
𝐹=
(1 + 𝑓)𝑛
Consider the same $1000 now, a 10% per year market rate, and
inflation rate of 4% per year, In 7 years, the purchasing power
will be
1000(1 + 0.10)7
𝐹=
(1 + 0.04)7
𝐹 = $1480.86
 INFLATION FW CALCULATIONS ADJUSTED FOR INFLATION

Case 3: Future Amount Required, No interest

𝐹 = 𝑃(1 + 𝑓)𝑛
This case recognizes that prices increase when inflation is
present. Simply put, future dollars are worth less, so more are
needed.
Reconsider the $1000 used previously. If it is escalating at
exactly the inflation rate of 4% per year, the amount 7 years from
now will be
𝐹 = 1000(1 + 0.04)7 = $1315.93
 INFLATION FW CALCULATIONS ADJUSTED FOR INFLATION

Case 4: Inflation and Real Interest

𝐹 = 𝑃(1 + 𝑀𝐴𝑅𝑅𝑓 )𝑛
This is the case applied when a MARR is established.
Maintaining purchasing power and earning interest must
account for both increasing prices (case 3) and the time value of
money
 INFLATION FW CALCULATIONS ADJUSTED FOR INFLATION

Case 4: Inflation and Real Interest

𝐹 = 𝑃(1 + 𝑀𝐴𝑅𝑅𝑓 )𝑛
For example, if the company has a WACC (weighted average
cost of capital) of 10% per year and requires that a project
return 3% per year and above its WACC, the real return is
i=13%. The inflation-adjusted MARR is calculated by including
the inflation rate of say 4% per year.

𝑀𝐴𝑅𝑅𝑓 = 0.13 + 0.04 + 0.13 0.04 = 17.52%

 INFLATION FW CALCULATIONS ADJUSTED FOR INFLATION

Example
Abbott Mining Systems wants to determine whether it should buy now
or buy later for upgrading a piece of equipment used in deep mining
operations in one of its international operations. If the company selects
plan A, the equipment will be purchased now for $200,000. However, if
the company selects plan I, the purchase will be deferred for 3 years
when the cost is expected to rise rapidly to $340,000. Abbott is
ambitious; it expects a real MARR of 12% per year. The inflation rate in
the country has averaged 6.75% per year. From only an economic
perspective, determine whether the company should purchase now or
later (a) when the inflation is not considered and (b) when inflation is
considered
Thank You for
Listening!
Any Questions?