Lester's just signed a contract that will provide the firm with annual cash inflows of €28,000, €35,000, and €42,000 over the next three years with the first payment of €28,000 occuring one year from now.
-> What is this contract worth today at a
discount rate of 7,25%?
Present Value (PV)= €28,000:(1+0,0725)
+€35,000:(1+0,0725)^2
+€42,000:(1+0,0725)^3
The Contract today is worth: €90,580.55.
Lisa's calculations should say:
Present value
= 28,000÷(1+0.0725)^1+35,000÷(1+0.0725)^2+42,000÷(1+0.0725)^3
or
= 28,000/(1+0.0725)^1+35,000/(1+0.0725)^2+42,000/(1+0.0725)^3
or
= 28,000(1+0.0725)^-1+35,000(1+0.0725)^-2+42,000(1+0.0725)^-3
= 90,580.55
The standard sign for division online is / if you cannot type the ÷
I have never seen : used as a division sign.
To calculate the present value of future cash flows, we can use the formula for the present value of an annuity. The formula is:
PV = CF₁ / (1 + r) + CF₂ / (1 + r)² + CF₃ / (1 + r)³
Where:
PV = Present value
CF₁, CF₂, CF₃ = Cash flows in each period
r = Discount rate
In this case, the cash flows are €28,000, €35,000, and €42,000, occurring one year from now, two years from now, and three years from now respectively. The discount rate is 7.25%.
Now we can substitute the values into the formula:
PV = €28,000 / (1 + 0.0725) + €35,000 / (1 + 0.0725)² + €42,000 / (1 + 0.0725)³
Using a calculator or spreadsheet software, we can calculate the present value:
PV ≈ €26,037.08 + €30,840.51 + €34,770.53
PV ≈ €91,648.12
Therefore, the contract is worth approximately €91,648.12 today at a discount rate of 7.25%.