Time Value of Money 1

Time Value of Money 3

Time Value of Money

Question 1: Future value (FV) of $100,000 for a period of 10 years from now

FVof a lump sum can be calculated by the compounding the present value at a given interest rate.FV= Present value (Principal) x (1+r) ^t, where present value=$100,000, r= interest rate and t= number periods (years).

a. FV at an interest rate of 2%=$100,000(1+0.02) ^10= $100,000×1.218994=$121,899.44

b. FV at an interest rate of 5%=$100,000(1+0.05) ^10= $100,000×1.6289466=$162,889.46

c. FV at an interest rate of 8%=$100,000(1+0.08) ^10= $100,000×2.158925=$215,892.50

d. FV at an interest rate of 10%=$100,000(1+0.10) ^10= $100,000×2.593742=$259,374.

Question 2: Present value of expected futurecash at 8% discounting rate

The present value (PV) = Future cash x discounting factor. PV= future cash x (1/(1+r)^t)), where r= discounting rate t= period(Brigham &Houston, 2016).

a) Year 1 present value= $100,000 x (1/ (1.08)0^1)) =$100,000×0.9259259=$92,592.59

b) Year 2 present value= $150,000 x (1/ (1.08)0^2)) =$150,000×0.8573388=$128,600.82

c) Year 3 present value= $200,000 x (1/ (1.08)0^3)) =$200,000×0.7938322=$158,766.44

d) Year 4 present value= $200,000 x (1/ (1.08)0^4)) =$200,000×0.7350299=$147,005.98

e) Year 5 present value= $150,000 x (1/ (1.08)0^5)) =$150,000×0.6805832=$102,087.48

f) Year 6 present value= $100,000 x (1/ (1.08) ^6)) =$100,000×0.6301696=$63.016.96

g) Year 7 present value= $100,000 x (1/ (1.08) ^7)) =$100,000×0.5834904=$58,349.04

h) Year 8 present value= $100,000 x (1/ (1.08) ^8)) =$100,000×0.5402689=$54,026.89

i) Year 9 present value= $100,000 x (1/ (1.08) ^9)) =$100,000×0.5402689=$50,024.90

j) Year 10 present value= $100,000 x (1/ (1.08) ^10)) =$100,000×0.4631935=$46,319.35

Question 3: present value at different discounting rates

a)Year 1 present value= $100,000 x (1/ (1.08)0^1)) =$100,000×0.9259259=$92,592.59

b) Year 2 present value= $150,000 x (1/ (1.06)0^2)) =$150,000×0.8889996=$133,349.94

c) Year 3 present value= $200,000 x (1/ (1.10)0^3)) =$200,000×0.7513148=$150,262.96

d)Year 4 present value= $200,000 x (1/ (1.04)0^4)) =$200,000×0.0.8548042=$170,960.84

e) Year 5 present value= $150,000 x (1/ (1.06)0^5)) =$150,000×0.7472582=$112,088.73

f) Year 6 present value= $100,000 x (1/ (1.04) ^6)) =$100,000×0.7903145=$79,031.45

g) Year 7 present value= $100,000 x (1/ (1.04) ^7)) =$100,000×0.7599178=$75,991.78

h) Year 8 present value= $100,000 x (1/ (1.04) ^8)) =$100,000×0.7306902=$73,069.02

i) Year 9 present value= $100,000 x (1/ (1.04) ^9)) =$100,000×0.7025867=$70,258.67

j) Year 10 present value= $100,000 x (1/ (1.04) ^10)) =$100,000×0.6755642=$46,319.

Summary

First Point

The value of $100,000 in 10 years to come depends on the compounding interest rate. At rate of 2% the amount will have accumulate an interest of ($121,899.44-$100,000) = $121,899.44. the future value increases as the interest rate is increasing, at an interest rate of 10 % the accumulated interest will be ($259,374.25-$100,000)=$159,374.25. According to this analysis, future value of money increases with an increase in interest rate(Brigham &Houston, 2016).

Second Point

The present value of money depends on the discounting rate and time. As time passes, money losses value,thus a dollar today is worth money than an expected dollar in future(Brigham &Houston, 2016). For example $100,000 expected in one year’s time is worth $92,592.59 in today’s dollars, while $100,000 expected in ten years from now is worth $46,319.35 in today’s dollar. Thus it is important for Genesis management to include the time value of money in decision making.

Third Point

A less discounting factor increases the present value of future cash flows, and also increase in the discounting period is reducing the present value of the expected cash flow. For example in question 2, the present value at year 10 at a discounting rate of 8 % is $46,319.35, while the value of the same amount at year 10 with discounting rate of 4% is $67,556.42. There is a difference of ($67,556.42-$46,319.35) = $21,237.07 due to change in interest rate from 8% to 4% for the same discounting period.