ConfirmedUser, Student, Bürokraten, Administratoren
589
Bearbeitungen
Financial Exercises 2: PV and Annuity: Unterschied zwischen den Versionen
Zur Navigation springen
Zur Suche springen
Financial Exercises 2: PV and Annuity (Quelltext anzeigen)
Version vom 24. Januar 2013, 19:09 Uhr
, 24. Januar 2013keine Bearbeitungszusammenfassung
(Die Seite wurde neu angelegt: „''by Clemens Werkmeister'' <html><img src=""http://vg06.met.vgwort.de/na/cc18daaac25b4d8ebfca7cc0baa16a4d"" width=""1"" height=""1"" alt=""</html> === 1. [[Ka…“) |
Keine Bearbeitungszusammenfassung |
||
| (3 dazwischenliegende Versionen desselben Benutzers werden nicht angezeigt) | |||
| Zeile 1: | Zeile 1: | ||
''by Clemens Werkmeister'' | ''by Clemens Werkmeister'' | ||
<html><img src="http://vg06.met.vgwort.de/na/cc18daaac25b4d8ebfca7cc0baa16a4d" width="1" height="1" alt=""</html> | |||
<html><img src= | |||
=== 1. [[Kapitalwert|Final value and present value]] === | === 1. [[Kapitalwert|Final value and present value]] === | ||
Pauline Miller has invested 1 | Pauline Miller has invested 1.000 € in securities that have a return of 5 % and can be sold – partially or completely – now or at the end of any year. <br/> | ||
a. Calculate the final value of the securities investment after two years.<br/> | a. Calculate the final value of the securities investment after two years.<br/> | ||
b. Pauline is offered the opportunity to invest 700 € in project A. The expected cash flows are 450 € in year 1 and 400 € in year 2. Calculate the value of Pauline’s assets at the end of year 2 if she transfers part of her securities investment to project A. Compare it to the securities-only investment.<br/> | b. Pauline is offered the opportunity to invest 700 € in project A. The expected cash flows are 450 € in year 1 and 400 € in year 2. Calculate the value of Pauline’s assets at the end of year 2 if she transfers part of her securities investment to project A. Compare it to the securities-only investment.<br/> | ||
| Zeile 17: | Zeile 16: | ||
=== 2. Perpetuities === | === 2. Perpetuities === | ||
a. What is the present value of a perpetuity of 10 | a. What is the present value of a perpetuity of 10.000 €/year at a discount rate of 7 €? <br/> | ||
b. What happens if the discount rate decreases to 6 % (best case) or increases to 8 % (worst case)?<br/> | b. What happens if the discount rate decreases to 6 % (best case) or increases to 8 % (worst case)?<br/> | ||
c. What is the discount rate that corresponds to a present value of 150 | c. What is the discount rate that corresponds to a present value of 150.000 €?<br/> | ||
=== 3. Growing perpetuities === | === 3. Growing perpetuities === | ||
a. An investment is expected to pay returns that start with 1 | a. An investment is expected to pay returns that start with 1.000 € in year 1 and later increase by 5 % per year. What is the present value of that investment assuming a discount rate of 10 %? <br/> | ||
b. What happens to the present value if the payment of the first return is delayed until year 3?<br/> | b. What happens to the present value if the payment of the first return is delayed until year 3?<br/> | ||
| Zeile 32: | Zeile 31: | ||
=== 5. Growing annuities === | === 5. Growing annuities === | ||
After retirement, you expect to live for 30 years and would like to have 50 | After retirement, you expect to live for 30 years and would like to have 50.000 € income each year. <br/> | ||
a. How much should you have saved in your retirement plan, if the plan assumes an interest rate of 6 %?<br/> | a. How much should you have saved in your retirement plan, if the plan assumes an interest rate of 6 %?<br/> | ||
b. What are the necessary savings if you want the annual income to increase by 2 % per year?<br/> | b. What are the necessary savings if you want the annual income to increase by 2 % per year?<br/> | ||
| Zeile 38: | Zeile 37: | ||
=== 6. Growing annuities === | === 6. Growing annuities === | ||
You plan to retire in 40 years and expect to need 800 | You plan to retire in 40 years and expect to need 800.000 € for living after retirement.<br/> | ||
a. How much would you need to save per year to achieve this goal? Assume an interest rate of 6 %.<br/> | a. How much would you need to save per year to achieve this goal? Assume an interest rate of 6 %.<br/> | ||
b. What happens if the interest rate drops to 5 %?<br/> | b. What happens if the interest rate drops to 5 %?<br/> | ||
| Zeile 44: | Zeile 43: | ||
=== 7. Mortgage payments === | === 7. Mortgage payments === | ||
Laureen Hardy has taken a 300 | Laureen Hardy has taken a 300.000 € mortgage on her appartment at an interest rate of 5 %. The mortgage calls for 15 equal annual payments, what is the amount of each payment?<br/> | ||
a. How much would you need to save per year to achieve this goal? Assume an interest rate of 6 %.<br/> | a. How much would you need to save per year to achieve this goal? Assume an interest rate of 6 %.<br/> | ||
b. Demonstrate the development of amortization and interest payments for the mortgage. How much is the amortization in year 1?<br/> | b. Demonstrate the development of amortization and interest payments for the mortgage. How much is the amortization in year 1?<br/> | ||
| Zeile 56: | Zeile 55: | ||
References:<br/> | References:<br/> | ||
For some useful formulae you might have a look at our [[Financial Resources Formulary]].<br/> | For some useful formulae you might have a look at our [[Financial Resources Formulary]].<br/> | ||
For further exercises we suggest | For further exercises we suggest our [[Financial Exercises]].<br/> | ||