Finance bonds/dividends/loans exercises, need help or formulas Some of the exercises, calculating the Ri is clear, but then i got stuck: A security pays a yearly dividend of 7€ during 5 years, and on the 5th year we could sell it at a price of 75€, market rate is 19%, risk free rate 2%, beta 1,8. What would be its price today? 2.1 And if its dividend growths 1,7% each year along these 5 years-what would be its price? A security pays a constant dividend of 0,90€ during 5 years and thereafter will be sold at 10 €, market rate 18%, risk free rate 2,5%, beta 1,55, what would be its price today? At what price have i purchased a security if i already made a 5€ profit, and this security pays dividends as follows: first year 1,50 €, second year 2,25€, third year 3,10€ and on the 3d year i will

Finance bonds/dividends/loans exercises, need help or formulas Some of the exercises, calculating the Ri is clear, but then i got stuck: A security pays a yearly dividend of 7€ during 5 years, and on the 5th year we could sell it at a price of 75€, market rate is 19%, risk free rate 2%, beta 1,8. What would be its price today? 2.1 And if its dividend growths 1,7% each year along these 5 years-what would be its price? A security pays a constant dividend of 0,90€ during 5 years and thereafter will be sold at 10 €, market rate 18%, risk free rate 2,5%, beta 1,55, what would be its price today? At what price have i purchased a security if i already made a 5€ profit, and this security pays dividends as follows: first year 1,50 €, second year 2,25€, third year 3,10€ and on the 3d year i will

Question
Ratios, rates, proportions
asked 2020-11-12
Finance bonds/dividends/loans exercises, need help or formulas
Some of the exercises, calculating the Ri is clear, but then i got stuck:
A security pays a yearly dividend of 7€ during 5 years, and on the 5th year we could sell it at a price of 75€, market rate is 19%, risk free rate 2%, beta 1,8. What would be its price today? 2.1 And if its dividend growths 1,7% each year along these 5 years-what would be its price?
A security pays a constant dividend of 0,90€ during 5 years and thereafter will be sold at 10 €, market rate 18%, risk free rate 2,5%, beta 1,55, what would be its price today?
At what price have i purchased a security if i already made a 5€ profit, and this security pays dividends as follows: first year 1,50 €, second year 2,25€, third year 3,10€ and on the 3d year i will sell it for 18€. Market rate is 8%, risk free rate 0,90%, beta=2,3.
What is the original maturity (in months) for a ZCB, face value 2500€, required rate of return 16% EAR if we paid 700€ and we bought it 6 month after the issuance, and actually we made an instant profit of 58,97€
You'll need 10 Vespas for your Parcel Delivery Business. Each Vespa has a price of 2850€ fully equipped. Your bank is going to fund this operation with a 5 year loan, 12% nominal rate at the beginning, and after increasing 1% every year. You'll have 5 years to fully amortize this loan. You want tot make monthly installments. At what price should you sell it after 3 1/2 years to lose only 10% of the remaining debt.

Answers (1)

2020-11-13
11) Total debt =€2850 x 10=€28500. I can amortize this amount in 5 years that means I make annual repayment of debt of €5700(Excluded interest element). My monthly payment shall be €475.(ex-interest). Now, we compute interest for 5 years on reducing balance of debt amount.
Year1:€28500x12%=€3420
Year2:€22800x13%=€2223
Year3:€17100x14%=€1596
Year4:€11400x15%=€855
Year5:€5700x16%=€912.
Till the term of 3.5years we paid €24000(including half year interest of €427,rounding off) Outstanding liability cum-interest comes to €9890(€2850+427+5700+912).
If I sell the Vespas to book a loss of 10% on my debt my selling price shall be, €8900(let 100% selling price be €9890 thus at 90% it comes to €8900)
[Assumption : it is assumed that interest amount accrues annully and can be spread over the months in a year.]
6) There can be 2 approach to this question: 1st by using the formula a)Dividend price approach b) Capital asset pricing model.
2nd by using the cost of equity which you derive using capital asset pricing model (CAPM) to discount the selling price at present rate.
I will solve this by the 1st approach.
Dividend price approach : Formula being ke=D1/P0+G, where D1 is annual dividend, P0 is current market value of equity (ex-dividend) and G is for Growth rate of dividend.
Capital asset pricing model (CAPM) : Formula : Rf+b(Rm-Rf)
Where Rf is risk free returns, b is the beta coefficient, Rm is market risk.
Let's find the cost of equity using CAPM method which comes to 0.1723 by using above state formula.
Now we replace Ke in dividend price approach to 0.1723 which gets us current market value of securities I.e €8.67 Working is as follows, As the dividend grows by 50% and 38% in year 2 and 3 respectively, we can average it to 44% Using the formula we get current market price as 13.67 reduce the profit you made and that shall be the cost you paid for the securities.
[Note that this approach ignores future market value of securities.]
Use the same formula in question 2 and 5 by making appropriate assumption and you will find your answers. Only thing to care about in question 2 is that in the 1st part you won't consider dividend growth rate, only in 2nd part it is required to be considered.
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