Corporate Finance

Corvinus University of Budapest Corporate Finance 2021 Fall Week 1 Present value, Future value – Regular cash flows Lecturers: Balázs Králik Nóra Felföldi-Szűcs Annuity: You have an annuity of 200 USD for 6 years. The yearly return is 3%. Calculate the PV of the annuity if the first cash flow you will receive is: • next year • tomorrow • 2022 Perpetuity: You have a yearly cash flow of 200 USD continuing forever. The yearly return is 3%. Calculate the PV of the CFs if it starts • next year, • tomorrow • 2024 Growing perpetuity: You have a yearly cash flow of 1000 HUF continuing forever. The cash flow has a growth rate of 5%. The yearly return is 10%. Calculate the PV of the CFs, if it starts • next year, • tomorrow • 2023 • Next year, but is only for 12 years Deposit 1.: You have an investment opportunity where you deposit 2 000 TEUR, and after 5 years you receive a single cash flow. • Calculate the final cash flow if the yearly return is 5%! • Calculate the yearly return if you receive a single cash flow of 2676.45 TEUR! Redemption plan: You have a loan of HUF 1.000.000 which you have to sink in 3 equal payments in the coming 3 years. The interest you have to pay is 6%. • Calculate the yearly payments. • Divide the CF into two parts: interest payment and capital redemption. • Assume that at the end of the first year the interest rate will be increased to 7%. Recalculate the redemption plan. Comparing cash flows – various payment frequencies 1: You have won a cash price and you can choose from the following three constructions of payments. Which one do you prefer when you are searching for the highest present value? The yield curve is flat at 8%. • 100,000 HUF today and an amount of 5% higher at the end of the coming years continuing for ever. • An annuity of five years is starting today. It pays 630,000 HUF. Corvinus University of Budapest Corporate Finance 2021 Fall • A growing perpetuity where you will receive the first cash flow equalling 400,000 HUF in ten years which will grow 4% per year. Comparing cash flows – various payment frequencies 2: Consider you have won a cash prize. You have the following opportunities. Which one would you choose? In the following table, you can find five possible cash flow plans. (On the horizontal header you can see the timing of cash flows (given in years).) As you need urgent money to cover your admission fee at a well-known MBA course, you decide to sell your cash price. The return is 8%. • Would you accept a proposal of 18 000 USD? • What do you think about the offer when the expected rate of return increases to 10%? Years 1. 2. 3. 4. 5. 1 2 3 4 6,000 2,000 2,000 2,000 2,000 2,000 1,850 1,850 600 630 662 695 5 6 7 8 9 6,000 2,000 2,000 2,000 2,000 2,000 1,850 1,850 1,850 1,850 1,850 729 766 804 844 886 …for 10 ever 10,000 2,000 1,850 1,850 42,747 930.8 977 Discount Factor in Excel: Prepare a chart where you illustrate how DF is changing. • Illustrate, how DF changes over time! Choose DF(2%,t), DF(6%,t) and DF(10%,t) and display them on the same chart where t takes the values from 0 to 10 years.) • Illustrate how DF changes with r! Choose DF(r,1), DF(r,5) and DF(r,10) and display them on the same chart where r takes the values from 0 to 10%.) Annuity Factor in Excel: Prepare a chart where you illustrate how AF is changing. • Illustrate how AF changes over time! Choose AF(2%,t), AF(6%,t) and AF(10%,t) and display them on the same chart where t takes the values from 0 to 10 years.) • Illustrate how AF changes with! Choose AF(r,1), AF(r,5) and AF(r,10) and display them on the same chart where r takes the values from 0 to 10%.) The relation of AF and DF in Excel: Prepare a table where you illustrate that AF is the sum of the appropriate DFs. Preparation for the 2nd week: Please revise what you learned about logarithm calculation! Be able to solve this kind of problems: Finally, we will calculate t if we know that the r=8% and Corporate Finance 2021 Fall Workbook Week 2 Net Present Value – Regular cash flows, returns and IRR Lecturers: Balázs Králik Nóra Felföldi-Szűcs A. SITUATIONS Bank Deposit: Your bank called you offering you special investment units for the 2,000 Euro you have in your current account, maturing after 5 years. • Calculate the final cash flow if the yearly return is 5%! • Calculate the yearly return if it pays out a single cash flow of 2,676.45 Euro! Your bank also offers you a 5 year restricted deposit account which pays interest monthly at its standard 4.9% pa. Would you prefer this one? Investment Product: expected return Your investment advisor offers you units of a special Morgan Stanley investment product which appears to return 5% pa. You later discover that his firm collects an up-front advisory fee of 3% when you invest Calculate what return you should expect: • in the first year • over 2 years Structured Product: expected return Your investment advisor offers you a Goldman Sachs “Protected” investment product which has a 50% chance of returning 10% pa and a 50% of returning 0% pa. Calculate what return you should expect: • in the first year • over 2 years • over 2 years if his firm takes a 4% fee up-front Mortgage Loan Schedule: You have taken out a loan on your house of HUF 10,000,000 which you have agreed to pay back in 3 equal installments over the coming 3 years. The interest you have to pay on the outstanding balance including unpaid interest is 6%. • Calculate the yearly payments. At the end of the first year, the bank increases the interest rate to 7%. Recalculate the redemption plan. • Calculate the balance outstanding by dividing the Cash Flow into two parts: interest payment and capital redemption • Calculate the new yearly payments. Preferential Loan and NPV: You are the CEO of the MagicSol Company. The firm offers loans on preferential term to employees who have been working for a minimum of 5 years at the company. The total volume of the outstanding loans is Corporate Finance 2021 Fall HUF 60 million, and those are offered at a yearly interest rate of 6%, while the average required return for similar loans on the market equals 10%. The loans will be sunk in 5 years, in equal payments at the beginning of each year. • Calculate the fair equal yearly payments. • Calculate the net present value of taking the loan at preferential term for the company. • Calculate the net present value (the total value of the corporate support to all the workers) of taking the loan at preferential term from the company. Pension Annuity Your uncle is about to retire and will receive an annuity from his employer’s pension fund of 10,000 USD pa or a lump sum of 120,000 USD. Your friend is an investment advisor who says Aon Life Assurance is offering a 20 year annuity with the lump sum which pays 8% pa, with no up-front fees. According to the latest actuarial tables for people of your uncle’s age and health, their life expectancy is 18 years. Calculate whether your uncle should or should not take the lump sum, assuming a cost of money of 5%, by calculating: • the expected present value of the pension annuity • the present value of the annuity bought with the whole lump sum • how much your uncle will benefit or lose out on by taking the lump sum Would you conclusion change if your uncle is confident he will live a further 22 years? How much extra would you pay Aon Life Assurance for life insurance to cover the possibility your uncle lives beyond 20 years? Monthly annuity: You have a stream of monthly cash flows of 20 EUR for 5 years. The yearly return is 6%. Calculate the PV of the annuity, if the first cash flow you will receive is • in 30 days • in 180 days Comparing payment constructions 1::You plan to purchase a flat. Which of the following options would you choose if your cost of capital is 10%? • HUF 18 million cash now. • HUF 9 million now and HUF 120 thousand per month for 10 years. (The first payment is due in a month.) • HUF 240 thousand per month for the next 10 years. (The first payment is due in a month.) • HUF 143 thousand rental fee per month for ever. (The first payment is due right now!) Comparing payment constructions 2: You are about to purchase a car. The following four constructions of payment is offered to you in the saloon. Choose the best for you. (The applicable cost of capital is 10 percent.) • HUF 4,5 billion cash. Corporate Finance 2021 Fall • HUF 950-950 thousand due in six following January (the first is to be paid right now) • HUF 2 billion right now, then over 36 month a monthly payment of HUF 82 thousand (these payments are due at the end of each month, the first one in a month). • Your old car with a value of HUF 1.3 billion will be taken over by the saloon. In exchange they will reduce the price of the new car by HUF 1.5 million. This option is only available if you take a debt for the remaining part (3 billion) at an interest rate of 14 percent for 6 years with equal monthly repayments (the first instalment is due in a month time). Cash Prize 1: You own a UK Government Premium Bond which randomly awards cash prizes to its bond holders each month. This month you have won one. The UK Government has offered you three ways to receive the prize. Which one do you prefer when you are searching for the highest present value? The yield curve is flat at 8%. • 100,000 HUF today followed by amounts 5% higher at the end of every subsequent year. • An annuity of five years is starting today, paying 630,000 HUF pa. • A perpetuity where you will receive the first cash flow equalling 400,000 HUF in ten years, growing thereafter at 4% per year Cash Prize 2: You bought some online scratch-cards from the Belgian National Lotto and won another cash prize! The Belgian Government is offering you various payment options (see table below). • Which one would you choose? As you need money urgently to cover your admission fee to a well-known MBA course, you decide to sell your prize but only your rich cousin is interested. • Would you accept her proposal of 18,000 USD, knowing that she currently receives 8% on her government investments? • Would you change your mind if you knew she receives 10%? Years Option 1 Option 2 Option 3 “Win For Life” Option 4 Option 5 2,000 1 6,000 2,000 600 2 3 4 2,000 2,000 630 6 2,000 5 6,000 2,000 1,850 1,850 662 695 7 8 9 2,000 2,000 2,000 2,000 1,850 1,850 1,850 1,850 1,850 729 766 844 886 804 10 10,000 2,000 10+ 1,850 42,747 930.8 1,850 977 Saving plans and returns: You decided to start saving to finance the future education of your children. You can choose from the following options: • • • • 1% monthly return in the coming 10 years, 12% yearly return in the coming 10 years, 3.5% quarterly return in the coming 10 years. Yearly returns for one year investments 10%, yearly returns for 1-5 five years investments 11% and yearly returns of 12% over an investment horizon of 5-10years. Corporate Finance 2021 Fall B. ASSIGNMENTS IRR in Excel: You have three projects. In the table below, you can find the cash flow plan for the evaluated projects. • Prepare a chart where you illustrate how NPV changes with the rate of return! (For example, you can choose r=0%-2%-4%...50%) • Based on the charts, estimate the IRR for the three projects. • Compare your estimation with the result of the Excel Function (IRR). • Think about the limits/difficulties of IRR calculation. t C1 C2 C3 1 2 3 4 5 6 -100 -200 -500 20 30 400 30 40 400 50 40 -1000 -10 40 1500 30 30 300 70 30 -400 C. PREPARATORY QUESTIONS FOR THE QUIZ • Explain the concept of Net Present Value rule. • If your future cash flows are fixed, how can your NPV change over time? • Present two investment opportunities, where NPV does not help you to make your investment decision. What are the general conclusions you can draw? • Define the formula for the effective return for one period. • Define the formula for the effective multivariate return. • Explain CAGR? • Define IRR. • You can apply for a bank loan at an IRR=5%. The average required return on bank loans at the market is 4.5%. Would you apply for the former construction? • List the difficulties of IRR calculation. Corporate Finance 2021 Fall Workbook Week 3 Valuing Bonds Lecturers: Peter Grace Nóra Felföldi-Szűcs Balázs Králik 1. Zero Coupon Bond: The yearly returns for the coming three years are 8%, 9% and 10%. a. Calculate the discount factors for the coming three years! b. Calculate the price of a zero coupon bond (face value=100) with a maturity of 1, 2 ad 3 years. year 1 2 3 fwd rate 8% 9% 10% discount rate 93% 85% 77% zero rate 8.000% 8.499% 8.997% zero price 92.5925926 84.9473327 77.2248479 2. Yield Curve: In the following table you can find the prices for zero coupon bonds. Maturity Price (%) 1 91,74% 2 82,64% 3 71,18% 4 65,87% a. What kind of a yield curve do you have? b. Price a Treasury Bond with a yearly coupon yield of 8% maturing in 4 years. year 1 zero price 91.74% zero yield 9.00% bond principal 1000, 8%coupon cf 80 discounted 73.392 PV 907.844 2 82.64% 10.00% 3 71.18% 12.00% 80 66.112 80 56.944 4 65.87% 11.00% humped curve 1080 711.396 coupon