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Presentation outline (10/01/2010)

Presentation outline (10/01/2010). Two approaches of comparing revenues Annuities Present value of cash flow repeated in perpetuity Future value of terminating annuity Multiple cash flow. Comparing approaches: Discounting vs Compounding.

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Presentation outline (10/01/2010)

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  1. Presentation outline (10/01/2010) Two approaches of comparing revenues Annuities Present value of cash flow repeated in perpetuity Future value of terminating annuity Multiple cash flow

  2. Comparing approaches: Discounting vs Compounding Suppose as a manager of Smallwood project in Siraha (GTZ assistance) you need to compare the project revenue (on per ha basis) under the following situation: • There is a natural regeneration of Sal, hence– no costs of establishment • There is a net revenue of Rs 500/ha accrued due to the first thinning in the 10th year of the project. • The second thinning will take place in 14th year with a net revenue of Rs 1000/ha. • The final clearing will take place in the 22nd year with a net revenue of Rs 8000/ha. • Compare the revenues of the project using compounding and discounting approaches at 5% interest rate.

  3. Two approaches of comparing revenues (r = 5%)

  4. Comparing two approaches 10375 (1.05)22 = 3547 Or, 3547 * (1.05)22 = 10375

  5. Annuities Annuity is series of equal payments/receipts over a specified number of periods Some examples are • House loan payments • Car loan • Insurance etc

  6. Annuities If one saves NRs 1000 a year at the end of every year for three years in an account earning 7% interest, compounded annually, how much he accumulates at the end of third year? FV3 = NRs 1000 (1.07)2 + NRs 1000 (1.07)1 = NRs 1000 (1.07)0 = NRs 3214.9

  7. PV of a cash flow lasting T years, then repeated in perpetuity PV∞ = PVT/ (1 – 1/ (1+r)T) PV∞ = PV of perpetuity The subscripts ∞ and T refer to duration of cash flow

  8. Future value of terminating annuity Interest rate = 4% Formula for calculating future value of annuity (1+i)n – 1 = i = (1+0.04) 30 -1 / 0.04 = $84.12

  9. Example of Annuity • For Southern Loblally Pine, annual property taxes will be $ 1.50 per acre. What will be the future value of the amount that is to be paid for 30 years if the cost of capital is 4%? • Annual property tax = $ 1.50 Compounding formula = (1.04)30 – 1 0.04 = $ 84.12 Present value of annuity = $ 25.93

  10. Present value of perpetual periodic annuity An uneven aged forest produces thinning products in every 10 years. Present value of a perpetual periodic is calculated by: a PV = (1+i)n – 1 Where, PV = present value of a perpetual annuity a=amount of annuity received in t years and every t years thereafter i= interest rate n=number of t years 1 Present value formula (1+i)n – 1

  11. Multiple cash flow A projected cash flow for an investment is $500 in first year, $600 at the end of second year and $10,700 at the end of the third year. For 5% discount rate, the value of this investment as of today is: PV1 = 476.19 PV2 = 544.22 PV3 = 9243.06 PV = 10263.47

  12. THANKS

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