Question

Please solve without the use of excel by discounting the cash flows "by-hand".

1. Find the FV of $10,000 33 years in the future if the opportunity cost rate is 8% (use Excel formulas and basic PV/FV techniques).

2. Find the PV of $1,000,000 to be delivered in 16 years if the opportunity cost rate is 7% (use Excel formulas and basic PV/FV techniques).

3. Would you prefer the following (you can use just formulas for this problem):

1. An ordinary annuity where you receive $500 each year for 20 years if the opportunity cost is 6%
2. An annuity due where you receive $480 each year for 20 years if the opportunity cost rate is 5.9%

4. What is the net present value of the following stream of cash flows assuming the opportunity cost rate is 12%? Solve NPV using each cash flow and the NPV function in Excel (use Excel formulas and basic PV/FV techniques).

Year 0:             -$10,000

Year 1:            $4,000

Year 2:            -$2,000

Year 3:            $5,000

Year 4:            $3,000

Year 5:            $6,000

Answer 1

Answer : 1) As required by you I have solved without using Excel :

Calculation of Future Value

Future Value = Present Value * (1 + rate)^number of year

= 10000 * (1 + 0.08)^33

= 10000 * 12.67605

= 126760.50

2.) Calculation of Present Value :

Future Value = Present Value * (1 + rate)^number of year

= 1,000,000 / (1 + 0.07)^16

= 1,000,000 / 2.952164

= 338734.60

3.) : FV of ordinary annuity = Periodic Payment * [ ( 1+ rate)^ no. of period - 1] / rate

= 500 * [ (1+0.06)^20 - 1 ] / 0.06

= 500 * 36.78559

= 18392.80

4.) FV of annuity due = (1+rate) * Periodic Payment * [ (1+ rate)^no. of pwriod - 1] / rate

= (1+0.059) * 480 * [ ( 1+0.059)^20 - 1] / 0.059

= 1.059 * 480 * 36.39259

= 18499.08

5.) Calculation of Net Present Value :

Year	Cash Inflow	Present Value Factor @12%	Present value of cash inflow
1	4000	0.892857143	3571.428571
2	-2000	0.797193878	-1594.387755
3	5000	0.711780248	3558.901239
4	3000	0.635518078	1906.554235
5	6000	0.567426856	3404.561134
		Total Present value of cash inflow	10847.05742
		Less : Cash outflow	10000
		Net Present Value	847.06