Decision Tree Table for choosing present and future value equations. ltem to Number of Present
or Annual or Perpetual or evaluate occurrences Future Equation to use Periodi Terminal Series
na na 0 value payment:s Future Present na na Periodic Annual Periodic Vn Vo(1+i)\"
Vo=Vn/(1+i)\" Vn=pl(1+i)n-1)/[(1+1)t-1)] Single Revenue Future Terminal Perpetual Vo=
p/[(1+i)\'-1] Series of Equal payments Present Terminal Vo (1-1(1+)-1](1+i)) Cost PerpetualVo
Annual Terminal Vo=p[(1+i)n-1)/[i(1+i)\") interest rate per year (in decimals) Vo = initial value
(in time 0) V- value in time n n total number of years of compounding or discounting considered
p = amount of payment occurring every t years t number of years in one multiyear group or
interval of years (length of the interval) Payments occur at the end of the period or multiyear
interval Please note: these equations can be used for months or weeks or any other length of time
as long as the interest rate is defined at that period, n is defined as total number of periods, and t
is the number of periods in one multiperiod group or interval. In this class, we will stick
primarily to using the annual rates. Source: Figure 7.3 from Davis, et al. 2001 Forest
Management, p. 341
Solution
a. As seen from the table,
Present value of perpetual periodic CF is = P/[(1+i)^t - 1]= 50000/[1.07^45 - 1] = 50000/(21.002
- 1)
= $2,499.69
b. Present value of a perpetual $100 tax = P/i = 100/0.07 = $1,428.57
Present value of the cash flow = 2,499.69 - 1,428.57 = $1,071.12
c. AS the asking price of the land is $1000 and is less than the NPV of $1,071.12 you should buy
it..
Decision Tree Table for choosing present and future value equations. .pdf
1. Decision Tree Table for choosing present and future value equations. ltem to Number of Present
or Annual or Perpetual or evaluate occurrences Future Equation to use Periodi Terminal Series
na na 0 value payment:s Future Present na na Periodic Annual Periodic Vn Vo(1+i)"
Vo=Vn/(1+i)" Vn=pl(1+i)n-1)/[(1+1)t-1)] Single Revenue Future Terminal Perpetual Vo=
p/[(1+i)'-1] Series of Equal payments Present Terminal Vo (1-1(1+)-1](1+i)) Cost PerpetualVo
Annual Terminal Vo=p[(1+i)n-1)/[i(1+i)") interest rate per year (in decimals) Vo = initial value
(in time 0) V- value in time n n total number of years of compounding or discounting considered
p = amount of payment occurring every t years t number of years in one multiyear group or
interval of years (length of the interval) Payments occur at the end of the period or multiyear
interval Please note: these equations can be used for months or weeks or any other length of time
as long as the interest rate is defined at that period, n is defined as total number of periods, and t
is the number of periods in one multiperiod group or interval. In this class, we will stick
primarily to using the annual rates. Source: Figure 7.3 from Davis, et al. 2001 Forest
Management, p. 341
Solution
a. As seen from the table,
Present value of perpetual periodic CF is = P/[(1+i)^t - 1]= 50000/[1.07^45 - 1] = 50000/(21.002
- 1)
= $2,499.69
b. Present value of a perpetual $100 tax = P/i = 100/0.07 = $1,428.57
Present value of the cash flow = 2,499.69 - 1,428.57 = $1,071.12
c. AS the asking price of the land is $1000 and is less than the NPV of $1,071.12 you should buy
it.
![Decision Tree Table for choosing present and future value equations. ltem to Number of Present
or Annual or Perpetual or evaluate occurrences Future Equation to use Periodi Terminal Series
na na 0 value payment:s Future Present na na Periodic Annual Periodic Vn Vo(1+i)"
Vo=Vn/(1+i)" Vn=pl(1+i)n-1)/[(1+1)t-1)] Single Revenue Future Terminal Perpetual Vo=
p/[(1+i)'-1] Series of Equal payments Present Terminal Vo (1-1(1+)-1](1+i)) Cost PerpetualVo
Annual Terminal Vo=p[(1+i)n-1)/[i(1+i)") interest rate per year (in decimals) Vo = initial value
(in time 0) V- value in time n n total number of years of compounding or discounting considered
p = amount of payment occurring every t years t number of years in one multiyear group or
interval of years (length of the interval) Payments occur at the end of the period or multiyear
interval Please note: these equations can be used for months or weeks or any other length of time
as long as the interest rate is defined at that period, n is defined as total number of periods, and t
is the number of periods in one multiperiod group or interval. In this class, we will stick
primarily to using the annual rates. Source: Figure 7.3 from Davis, et al. 2001 Forest
Management, p. 341
Solution
a. As seen from the table,
Present value of perpetual periodic CF is = P/[(1+i)^t - 1]= 50000/[1.07^45 - 1] = 50000/(21.002
- 1)
= $2,499.69
b. Present value of a perpetual $100 tax = P/i = 100/0.07 = $1,428.57
Present value of the cash flow = 2,499.69 - 1,428.57 = $1,071.12
c. AS the asking price of the land is $1000 and is less than the NPV of $1,071.12 you should buy
it.](https://image.slidesharecdn.com/decisiontreetableforchoosingpresentandfuturevalueequations-230702063440-de1dee29/85/Decision-Tree-Table-for-choosing-present-and-future-value-equations-pdf-1-320.jpg)
