# Thread: Is my investment profitable?

A sum of $20000 is invested in equity shares of XYZ CORPORATION for a period of 10 years.If the market value of this investment became$51875 after 10 years and the interest is reckoned continuously @10 percent per year, show that the investment become profitable if it gives a shareholder a dividend yield of 3% per year for 10 years. Ans: Dividend of 3% of $20000=$600 $(A)\large PV_{10} \of \ the \ dividend \ income \ stream =\int_{0}^{10} 600 e^{-rt}dt, \ r=0.1$ $=\frac{600}{0.1}\left[-e^{-0.1t}\right]_{0}^{10}$ $={6000}\left[1-e^{-1}]$=3792.72335(B)Present value of market value of $51875 after 10 years = $\frac{51875}{e^1}=19083.75$Thus, the total present value calculated in (A) and (B)[22876.47] is greater than the initial investment amount$20000. So we can say investment of $20000 in XYZ CORPORATION is profitable.Are my calculations right?Let me know from this forum. 2. ## Re: Is my investment profitable? Yes, your calculations are correct. However, did you realise that using 10% annually (no compounding) means: 51875 / 1.10^10 =$20,000 present value (instead of 19,083.75).

And the present value of the dividends: 600(1 - 1/1.10^10) / .10 = $3,686.74 So why go to the contortions of compounding interest when looking at an estimate over a long period (10 years), when all sorts of fluctuations can occur. Btw, "compounding continuously" sounds GREAT.... but compare it to "cpd. daily" using a million dollars over 1 year: 1,105,170.92 (continuous) 1,105,155.78 (daily) A difference of$15.14 !!