Present Value Calculations

Present Value Calculations

  1. 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 2nd 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  ]
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).

 

  1. 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  ]
P V  =  $ 12600  x   [ 0.89]
P V  =  $ 11214

(Moyer, Kretlow and McGuigan, 2011)

 

 

  1. 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
    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

 

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. 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

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.

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