Apply Time Value Concepts - Series 65

1. Compute $PV$ of a perpetuity paying $PMT=100$ per year at $r=10\%$.

   $1000$. Divides the constant annual payment by the discount rate to value the infinite payment stream.

2. State the formula for NPV given cash flows $CF_t$ discounted at rate $r$.

   $NPV=\sum_{t=0}^{n}\frac{CF_t}{(1+r)^t}$. NPV aggregates the discounted values of all cash flows from inception to calculate the net value added by the investment.

3. Compute $NPV$ at $r=10\%$ for $CF_0=-1000$ and $CF_1=1100$.

   $0$. The discounted inflow exactly offsets the initial outflow, indicating breakeven at the given rate.

4. Find $FV$ for $PV=1000$, $r=10\%$, $n=2$ with annual compounding.

   $1210$. Compounds the initial amount at the annual rate over two periods to reach the accumulated value.

5. Identify the sign of NPV when the discount rate $r$ is above the project IRR (conventional cash flows).

   $NPV<0$ when $r>IRR$. For conventional projects, discounting above IRR overvalues costs relative to benefits, yielding negative NPV.

6. State the defining condition for IRR in terms of NPV and cash flows.

   $0=\sum_{t=0}^{n}\frac{CF_t}{(1+IRR)^t}$. IRR is defined as the discount rate that equates the present value of cash inflows and outflows to zero NPV.

7. Compute $NPV$ at $r=10\%$ for $CF_0=-1000$ and $CF_1=1200$.

   $\frac{1200}{1.10}-1000\approx90.91$. Discounts the future inflow and subtracts the initial cost to find the net value added.

8. State the relationship between annuity due value and ordinary annuity value at rate $r$.

   Annuity due $=$ ordinary annuity $\times(1+r)$. Annuity due shifts payments one period earlier, equivalent to compounding the ordinary annuity value by one additional period.

9. Identify the sign of NPV when the discount rate $r$ is below the project IRR (conventional cash flows).

   $NPV>0$ when $r<IRR$. For conventional projects, discounting below IRR undervalues costs relative to benefits, resulting in positive NPV.

10. Identify the decision rule for NPV when the required return (hurdle rate) is $r$.

    Accept if $NPV>0$; reject if $NPV<0$. Positive NPV signals value creation above the cost of capital, while negative NPV indicates value destruction.

11. Find the IRR for $CF_0=-1000$ and $CF_1=1100$ (one-period project).

    $10\%$. Solves for the rate where the discounted inflow equals the outflow, setting NPV to zero.

12. Identify the decision rule for IRR relative to the required return $r$.

    Accept if $IRR>r$; reject if $IRR<r$. Projects with IRR exceeding the hurdle rate generate returns above the required threshold, justifying acceptance.

13. Find $PV$ for $FV=1210$, $r=10\%$, $n=2$ with annual compounding.

    $1000$. Discounts the future amount back two periods at the annual rate to determine its current equivalent.

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