Present Value Calculations
A. Suppose your bank account will be worth $15,000.00 in one year. The interest rate (discount
rate)
that the bank pays is 7%. What is the present value of your bank account today? What would
the present
value of the account be if the discount rate is only 4%?
The present value (PV) formula for the single amount is:
P V = F V ( 1 + I ) -n ( OR ) P V = F V x [ 1 ÷ ( 1 + I ) n ]
Using the 2 nd version of the formula, the calculations are
P V = F V x [ 1 ÷ ( 1 + I ) n ]
P V = $ 15000 x [ 1 ÷ ( 1 + 0.07 ) 1 ]
P V = $ 15000 x [ 1 ÷ ( 1.07 ) 1 ]
P V = $ 15000 x [ 1 ÷ 1.07 ]
P V = $ 15000 x [ 0.93458]
P V = $ 14018.70
If the interest is reduced to 4%
P V = F V x [ 1 ÷ ( 1 + I ) n ]
P V = $ 15000 x [ 1 ÷ ( 1 + 0.04 ) 1 ]
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P V = $ 15000 x [ 1 ÷ ( 1.04 ) 1 ]
P V = $ 15000 x [ 1 ÷ 1.04 ]
P V = $ 15000 x [ 0.96154]
P V = $ 14423.10
(Ross, Westerfield and Bradford, 2010).
B. Suppose you have two bank accounts, one called account A and another Account B.
Account A will be worth $6,500.00 in one year. Account B will be worth $12,600.00 in two years.
Both accounts earn 6%
interest. What is the present value of each of these accounts?
Account A.
P V = F V x [ 1 ÷ ( 1 + I ) n ]
P V = $ 6500 x [ 1 ÷ ( 1 + 0.06 ) 1 ]
P V = $ 6500 x [ 1 ÷ ( 1.06 ) 1 ]
P V = $ 6500 x [ 1 ÷ 1.06 ]
P V = $ 6500 x [ 0.9434]
P V = $ 6132.10
Account B
P V = F V x [ 1 ÷ ( 1 + I ) n ]
P V = $ 12600 x [ 1 ÷ ( 1 + 0.06 ) 2 ]
P V = $ 12600 x [ 1 ÷ ( 1.06 ) 2 ]
P V = $ 12600 x [ 1 ÷ 1.1236 ]
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P V = $ 12600 x [ 0.89]
P V = $ 11214
(Moyer, Kretlow and McGuigan, 2011)
C. Suppose you just inherited an gold mine. This gold mine is believed to have three years
worth of
gold deposit. Here is how much income this gold mine is projected to bring you each year for
the next
three years:
Year 1: $49,000,000
Year 2: $61,000,000
Year 3: $85,000,000
Compute the present value of this stream of income at a discount rate of 7%. Remember, you
are
calculating the present value for a whole stream of income, i.e. the total value of receiving all
three
payments (how much you would pay right now to receive these three payments in the future).
Your answer
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should be one number – the present value for this gold mine at a 7% discount rate but you have
to show
how you got to this number.
Now compute the present value of the income stream from the gold mine at a discount rate of
5%, and at
a discount rate of 3%. Compare the present values of the income stream under the three
discount rates
and write a short paragraph with conclusions from the computations.
Gold mine
Year/s Future
value
interest
rate
Step 1 Present
value
1 49000 7 1.07 45794.39252
2 61000 7 1.1449 53279.76242
3 85000 7 1.225043 69385.31954
Total 168459.4745
1 49000 5 1.05 46666.66667
2 61000 5 1.1025 55328.79819
3 85000 5 1.157625 73426.19588
Total 175421.6607
1 49000 3 1.03 47572.81553
2 61000 3 1.0609 57498.35046
3 85000 3 1.092727 77787.04105
Total 182858.207
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The higher the rates the lower the present values obtained and also the lower the rates the
higher the present value.
Part II: Read the following three sample business plans:
Ice Dreams
R J Wagner & Associates Realty
Interstate Travel Center
Which of these three projects do you think should have the highest risk from the point of view of
investors (potential providers of funds) and would therefore be evaluated using the highest
discount
rate? Which one do you think should have the lowest? Write a paper explaining your reasoning.
In your assessment of the business plans consider the possible risk of each plan. Risk is one of
the
main considerations when deciding whether a plan should be evaluated and discounted to
present value
using a high or a low discount rate.
Note: you are not expected to fully analyze the numbers and financial statements in these
business
plans. There are only forecasts and projections. Nobody really believes them anyway. Use your
intuition
rather than calculations to assess risk and potential of each of these plans.
R J Wagner & Associates Realty, Inc. is a new company that targets provision of high level
expertise in home ownership sales and purchases. It mainly focuses on home buyers and sellers.
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To fund its activities, it charges a commission on all its dealings. R J Wagner & Associates
should have the highest discount rate as its business that deals in real estate properties which
have very high rates of appreciation. Real estate properties rarely depreciate in fact their values
increases as time passes. They also face a lot of risks as their interest rates increases depending
on the bank’s interest’s lending rates that’s normally affected by the progress of the national
economy.
Interstate Travel Agency is actually intended to be a modern major center for travelers in Dallas,
Texas. It plans to build a convenience store, gas or diesel points, restaurant and other amenities
for travelers. Interstate Travel Agency would have a discount interest rating that’s lower than R J
Wagner as its business is relatively stable and the number of travelers rarely changes drastically.
The numbers of travelers are seasonal but are relatively constant and predictable. The risks
involved are relatively low as travelers will always most certainly be travelling every season.
Ice Dreams is a company that specializes on the provision of skating facilities including Ice
fields, skating boards, training, competition and also entertainment. This is a sporting activity
center that has its own calendar and which most likely will not be changing its activities and
events in the near future. It should actually enjoy the lowest rating as it’s the most stable business
of the three businesses. Its income is relatively constant and its risk factors are very low. Every
year it recruits new members just as the population is increasing its also having a constant stream
of clients.
References
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Ross, S., Westerfield, R, Bradford, D. (2010). Fundamentals of Corporate Finance (9 Ed.). New
York: McGraw-Hill.
Moyer, C., Kretlow, W., McGuigan, J. (2011). Contemporary Financial Management (12 Ed.).
Winsted: South-Western Publishing Co.
