Corporate Finance Practice Problems
If you put $1,200 into a money market account that earns 2.8% annually, but compounds quarterly. What will you have at the end of one year? 3 years?
$1,200 * (1 + .028/4) = 1208.4 * (1.007) = 1216.859 * (1.007) = 1225.377 * (1.007) = 1,233.95 3 Years, same process, but 12 times instead of 4 = 1,304.77 instead of annual compounding after 3 years of 1,303.65
You invested in equity that will convert to debt. You put in $10,000 that grew by 8%, -22%, 16%, 32%, and -13% over the first five years. Then it will grow by a fixed 5.5% for the next 10 years before paying out. What will it be worth at the end of that period
$10,000 * 1.08 * .78 * 1.16 * 1.32 * .87 * 1.055^10 = 19,168.76
If a savings bond pays 4% interest and you paid $500 for it, how long will it take to reach its face value of $1,000?
$500 * 1.04 = 520 *1.04 = 540.80... in the 18th year = 1,012.91
A machine is expected to generate $18,000 in cash flow year one. The cash flow will grow by 20% the next year, then 15%, 13%, and 8% in the subsequent years. At the end of that time we will sell the machine for salvage value of $5,000. If the cost of the machine is $65,000 and our cost of capital is 10%, should we do it?
0 1 2 3 4 5 Cash Flow -65000 18000 21600 24840 28069.2 35314.736 DCF -65000 16363.636 17851.24 18662.66 19171.641 18823.066 NPV = 4,312.04
You are investing in a financial instrument that costs $8,000. Every year it is to grow by 4.5%, half of the growth is paid out as a dividend, the other half is reinvested. At the end of 5 years you get the last dividend and the remaining balance paid out. Show that at a discount rate of 4.5% this is a negative NPV investment due to the lack of compounding of dividends?
0. 1 2. 3. 4 5 Balance 8000 8180 8364.05 8552.241 8744.667 8941.422 Dividend 180 184.0. 188.191 192.425 196.755 Cash Flow. -8000 180 184.05 188.191 192.425 9138.177 DCF -8000. 169.01 162.27 155.79 149.58 6669.78 NPV= -693.57
You are investing in a company paying dividends of $1 next year that will grow by 24%, then 20%, then 15%. At the end of that you plan on selling the stock for $60. What would you pay for it now if you expect a return of 9.5%?
1 2 3 4 Cash Flow $1 1.024 1.229 61.413 DCF .913 .854 .936 42.717 Pay $45.42 or less
A company will start paying dividend of $1.27 in 4 years. They intend to pay that same dividend forever. What is the price in time three, and therefore what is the price now (two different numbers) at a discount rate of 11.2%. What if it grows in perpetuity at 3.4% after year 4?
1 2 3 4 5 0 0 0 1.27 1.27 .... P3 = 1.27/(.112) = 11.34 so P1 = 11.34/(1.112)^3 = 8.25 ONLY WORKS THIS WAY BECAUSE THERE ARE NO DIVIDENDS IN 1, 2, OR 3 OTHERWISE THOSE WOULD NEED TO BE ACCOUNTED FOR P3 = 1.27/(.112-.034) = 16.28 and P1 = 16.28/1.112^3 = 11.84
If you were offered a contract such as this would you take it? You pay $50,000 now. At the end of years 1, 3, and 5 you will receive $30,000 at a required rate of return of 12%.
1 2 3 4 5 30000 0 30000 0 30000 30000/1.12 + 30000/1.12^3 + 30000/1.12^5 = 26,785.714+21,353.407+17,022.806=65,161.927 NPV is 15,161.93, DO IT!
Invest $1,000 at 2.3%, what will it be worth at the end of 12 years?
1,000 X 1.023 = 1,023 * 1.023 ... = 1,313.73 Or 1,000 X (1 + .023)^12 = 1,313.73
A company is going to pay dividends of $1.50, $1.00, and then $4.50 over the next three years before going bankrupt. What is the stock worth now if the expected return is 8.5%?
1.5/1.085 + 1/1.085^2 + 4.5/1.085^3 = 1.382+0.849+3.523 = $5.76
You put $10,000 into an IRA and it has earned 4%, 5.66%, -1.3%, and 12.8% over the past four years. What is it worth now?
10,000 * (1 + .04) = 10,400 * (1.0566) = 10,988.640 * (1 + (-.013)) = 10,845.788 * 1.128 = 12,234.05 negative growth, still add
You will be receiving $10,000 in 5 years. At a discount rate of 4.5%, what is it worth today.
10,000/(1.045)^5 = 8,024.51
1. You will be receiving $10,000 in 5 years. At a discount rate of 4.5%, what is it worth today. What if you had the same set up as #1, but you receive $10,000 each year instead of just year 5.
10,000/1.045+10,000/1.045^2+10,000/1.045^3+10,000/1.045^4+10,000/1.045^5 = 9,569.378+ 9,157.300+8,762.966+8,385.613+8,024.510 = $43,899.77
You are looking at buying a CD that pays a 3% annual rate. If you put in $1,000 for 3 years, what is the present value at a discount rate of 2%? What about at a discount rate of 4%?
1000*1.03^3 = 1,092.73/1.02^3 = 1,029.701 @4% discount 1092.73/1.04^3 = 971.42
You have put $800 into a project that has two possibilities. It will either grow your money by 4% per year for 6 years, or it will not grow at all until year 4, but then it will grow by 8% for 4 years. What are the two possible outcomes?
800 * 1.04^6 = 1,012.26 800 * 1.08^4 = 1,088.39 Remember this is 8 years out and the other you got after 6 so the better one is dependent on the discount rate bringing them back to present.
You have a perpetuity that will pay you $4,000 per year forever. What is it worth today if R=6%? What if it pays you $4,000 a month instead (divide R by 12)?
P0 = D1/(R-g) = 4000/(.06-0) = $66,666.67 Per month = 4000/(.06/12) = $800,000