UT FIN 357 - Chapter 4. Discounted Cash Flow Valuation v4 (70 pages)

Discounted Cash Flow Valuation Chapter 4 Finance 357 J David Miller 2017 Future Value Most projects in the real world involve decisions about the future Project Cost 100 000 today Benefit 105 000 in one year Would you suggest that your company accept the project 2 J David Miller 2017 Finding Present Value Project Cost 100 000 today Benefit 105 000 in one year Suppose the interest rate was 7 We can move the benefit back to today by discounting it to find the present value PV 105 000 1 7 98 130 84 The net benefit today would be 100 000 98 130 84 1 869 16 We call the net benefit today the net present value NPV 3 J David Miller 2017 Net Present Value The net present value or NPV is the present value of cash flows we receive minus the present value of cash we must pay out The book uses the formula NPV Cost PV Using the previous example we were told that the cost was 100 000 today and we found that the present value that we would receive was 98 130 84 NPV 100 000 98 130 84 1 869 16 4 J David Miller 2017 Net Present Value Decision Rule The NPV Decision Rule says that we accept projects if they have a positive NPV If we must decide between multiple projects we accept the project with the greatest NPV This is a fundamental rule of finance 5 J David Miller 2017 Net Present Value Problem A year ago you developed an app that you believe will revolutionize the dry cleaning industry You are already so busy managing the business that you barely have time for school The app is currently being used by 350 dry cleaning businesses A larger mobile app company has offered to buy the business for 1 000 000 once it is being used by 500 businesses At the rate it is growing that will be at the end of two years However if you hired a professional manager who would cost 100 000 in salary you believe that it would reach that level at the end of one year Should you continue to manage the business yourself or hire the manager 6 J David Miller 2017 Net Present Value Problem A year ago you developed an app that you believe will revolutionize the dry cleaning industry You are already so busy managing the business that you barely have time for school The app is currently being used by 350 dry cleaning businesses A larger mobile app company has offered to buy the business for 1 000 000 once it is being used by 500 businesses At the rate it is growing that will be in two years However if you hired a professional manager who would cost 100 000 in salary you believe that it would reach that level in one year Interest rates are 6 Should you continue to manage the business yourself or hire the manager Manage the business yourself Year Hire a manager Cash Flow 1 0 2 1 000 000 Year 1 Cash Flow 100 000 1 000 000 You should always draw a chart of your cash flows 7 J David Miller 2017 Net Present Value Problem Interest rate is 6 Manage the business yourself Year Hire a manager Cash Flow 1 0 2 1 000 000 Year 1 Cash Flow 100 000 1 000 000 Manage yourself Hire a manager NPV 1 000 000 1 06 2 NPV 100 000 1 000 000 1 06 1 NPV 1 000 000 1 1236 NPV 900 000 1 06 NPV 889 966 40 NPV 849 056 60 Disregarding your grades it is best to manage the business yourself Would this change if interest rates were 15 8 J David Miller 2017 Compounding The process of leaving money in an investment and allowing it to grow over multiple periods is called compounding We invest 1000 in a bank account that has an interest rate of 5 per year At the end of year 1 it is worth 1050 This is called simple interest Leaving the money in the account for the second year allows it to grow by 5 again However this time we are starting year two with 1050 We are earning interest on our previously earned interest 9 J David Miller 2017 Another View of Compounding Another way to accomplish this is to combine the steps By combining the process into one step we are calculating compound interest Which equals the formula for a cash flow that is compounded over multiple time periods T the number of time periods over which the money is invested 10 J David Miller 2017 Compounding Example A stock you own currently pays a dividend of 1 50 per share The dividend is expected to grow by 20 per year for the next 5 years How much will the dividend be 5 years from now 11 J David Miller 2017 Compounding Example A stock you own currently pays a dividend of 1 50 per share The dividend is expected to grow by 20 per year for the next 5 years How much will the dividend be 5 years from now Method 1 Formula FV 1 5 1 2 5 3 73 Method 2 Financial Calculator PV 1 5 N 5 FV 3 73 12 J David Miller 2017 I Y 20 FV Is it true Compound interest is the greatest force in the universe Attributed to Albert Einstein 13 J David Miller 2017 Discounting With a little simple algebra the compounding formula turns into the discounting formula A lottery winner will receive 1 000 000 4 years from today How much is the prize worth today using a 5 discount rate 14 J David Miller 2017 Lottery Value Today A lottery winner will receive 1 000 000 4 years from today How much is the prize worth today using a 5 discount rate Method 1 PV 1 000 000 1 05 4 823 045 Method 2 FV 1 000 000 I Y 5 N 4 PV 15 J David Miller 2017 1 000 000 1 215 Effect of Change in Discount Rate 15 Discount Rate Value 284 Present Value Left 5 Discount Rate 645 Present Value Left 16 J David Miller 2017 Cash Flow Example You win a lottery with a prize that is paid out over time and in varying amounts In 1 year you will be paid 4 000 in year 2 3 000 and in year 3 2 000 What is the present value of the prize if you could earn 4 in a bank account 17 J David Miller 2017 Year Cash Flow 1 4 000 2 3 000 3 2 000 Present Value of Cash Flows Year Cash Flow 1 4 000 2 3 000 3 2 000 Year 1 Year 2 Year 3 Present Value 18 J David Miller 2017 Valuing a Stream of Cash Flows II Nike is considering entering the Frisbee golf business Management at Nike is unsure whether this is a good business idea Market analysts expect Nike to generate the following expenses and revenues if it enters …