My apologies if this question has been asked before, i tried looking.
Alright, so i have a simple question, i wanted to ask just to make sure i'm on the right track here. Say we invest $\$1.000.000$, into something, and we expect our first cash inflow of $50.000$ to arrive $3$ years later. This amount of money will continue to grow by 4 %, and continue for ever. Lets just say the discount rate is $10 \%$
The way i though about this is to first discount the cash inflow, by 3 years. And then use the formula for a growing annuity, and find the NPV. This is the equation i setup.
$$\$1.000.000-\left(\left(\frac{\$50.000}{e^{0.1*3}}\right)\left(\frac{1}{1-\frac{1.04}{e^{0.1}}}\right)\right)$$
Does it seem right. I've never got an intuitive understanding of a annuity in perpetuity so I'm still fudging around with the formula. The reason I'm unsure is because if i discount the first cash inflow of $50.000 won't that mess up my calculations?
A thousand thanks in advance.
Isn't your discount rate on an annual basis, so discounting $50,000$ for three years is worth $50,000 \cdot 0.9^3$? Then the present value of the cash flow for year $n$ is $50,000 \cdot 1.04^{n-3}\cdot0.9^n$ This is a geometric series with starting value $50,000 \cdot 0.9^3$ and ratio $1.04 \cdot 0.9$, so sum it. Note that we have not used the amount invested, we have computed the value of the cash flow. You can compare that to the amount invested to see if the investment is profitable under these assumptions. I find it is quite unprofitable.