Value of the Future Stream of Cash Flows Equals Value of the Discounted Amounts of These Cash Flows
If the bank is paying 4% annual interest rate on the banking account, the present value of the future $1,250 in one years is worth today
PV = FV/(1 + r)
And thus future value of $1,250 with the discount rate of 4% is approximately $1,202.
Account A is earning 6% interest yearly and will be worth $3,000 in one year, employing the mentioned above formula, the present worth of this account is $2,830. Account B. is earning the same 6% yearly interest rate and will be worth $4,000 in two years. Present value of this future payment can be calculated employing the following formula:
PV = FV/(1 + r)^
Future value is discounted by the 6% interest rate foregone by two years and that is why it is necessary to use square root of the discount rate. So, the present value of the Account B. payment of $4,000 in two years is worth today $3,560.
Assuming that I have inherited an oil well which is expected to have life of three years untill it dries out and thus is expected to generate three more cash flows.
Year 1: $260,000
Year 2: $310,000
Year 3: $420,000
The discount rate for this stream of income is 7% and the present value of this steram of cash flows is calculated using the following formula:
PV = CF1/(1 + r) + CF2/(1 + r)^2 + CF3/(1 + r)^3
Thus, the present value of this stream of cash flows equals sum of present values of these cash flows. As cash flow two occurs in the second year from now, it must be discounted by (1 + r)^2 as this is the worth of this cash flow in todays money. The value I would agree to pay now to receive this stream of cash flows is $856,600.
Discount rate used in computing the present worth of the cash flows to be received from any investment opportunity is the interest forgone if having invested in this plan rather than in other plan. For example, if you can earn 7% annual interest on an investment opportunity, but you do not choose to do so and invest in something else, the actual true present value of the cash flows to be received from the second opportunity is worth 7% less each year to you due to opportunity foregone by having chosen the second opportunity.
Investment decision is used depending on the risks associated with investment initiatives and how the investor perceives the investment plan to be risky. If the investor perceives the plan to have low risk and he believes cash flows have big opportunity of occuring, the discount rate used to compute the present value of these cash flows will be lower than the discount rate used for other investment opportunities. Discount rate is the opportunity foregone and can be also viewed as required rate of return for the investor. Simple logic suggests that no investor will be willing to give up his funds for an initiative yielding 5% annual interest if he has access to investment opportunity with the same risk level but yielding 7% annual interest.
Investor would need to be motivated by higher possible rates of return for the riskir investments as majority of the investors are risk-averse with their different risk aversion rates. Plan that has some chance of not brinning any positive income for the investor would need to be given higher rates of risk in order to arrive at Net Present Value etimate for this initiative, which is the fair investment attractiveness measure. For example, one plan is very promising but has many risks associated with achieving it, the other initiative is not that promising and income is not expected to be as high, while the risks are much lower. Thus, the Net Present Value of the second initiative can be higher than for the first one and will be more acceptable for the investor.
Discount rate accumulates risk free rate of return, or the interest that could be generated with no risk at all, and is usually the interest rate on the government bonds with appropriate date to maturity. Then, the risk premium for the economy development (in case of international investments), risk premium for the region economic development in case the project is competing only within the region, risk premium for the city for innercity projects, risk premium for the industry development within which the project is likely to find competitors as industries are prone to be performing based on specific economic development, and risk premium for the project itself which is based on the project business plan, management of the project chosen, financing of the project and other things which can turn a very successfull on paper project into a complete faiure in practice.
In terms of proposed projects, Lansing Aviation is likely to be competing first on the regional level and provide aviation services within state. The proper decision on the discount rate for this project depends on the competition level within aviation industry and the niche that this project is likely to take based on its' competitive advantages and fair lack of such services within the industry. If Lansing Aviation project is aimed at servicing elite clients, it can be a very risky project as majority of corporations have either their own jets or have corporate contracts with existing airlines. Number of business class seats in jets can be reflective of the real demand for such services. Also, direction of the planned flights is also important as some are more demanded and thus competition among these services is much higher than for the other.
Adorable Pet Photography is a very income sensitive project as it is not going to provide clients with the product of necessity needs and demand for it will be correlated with income within the region. If the project is initiated in very high-income area with many families who have pets, which can be traced within animal hospital, the project is likely to have a high market capture and can be very successfull, thus the discount rate for it will be rather low comparing with the projects associated in the same region but that will have many competitors providing comparative services.
Take Five Sport Bar is the project that is likely to be demanded within area accomodating many men keen of football who would find attractive following sports games in a company of friends. If very well thought over, the project can be very successfull in this area, while it can be a complete failure in the area accomodating mostly old people or white collar workers who have low preferences for such services. The demand for this project is also likely to be associated with seasonal football games and thus the bar can be completely empty during summer when there are almost no games. The diversification strategy for such bar must be worked out in order to be receiving steady incomes.
I would advice to use the same discount rates for the Lansing Aviation and Adorable Pet Photography projects as both of them have their specific risks. The former may be a failure due to high competition and economies of scale that can be used by big aviation companies but cannot be advantaged from by the project. The latter is very sensitive to income and specific in demand. I would employ higher discount rate for the sports bar project as it is very seasonal and a very niched one. It is necessary to stress, that detailed market analysis must be made for the environment for each project, demand for such services, competitive advantages of each project in relation to comparables and further on to arrive at correct estimation.
In terms of potential, everything depends on the business plan and even though the market can be already taken for such services, if providing new and well promoted same services stressing higher than usual quality, the clients can be taken over. Adorable Pet Photography seems to have highest potential in terms of giving the market a very new product, but in my view the services must be diversified and good promotion campaign must be worked out in order to succeed. Lansing Aviation seems a project with low potential due to reasons mentioned above while sport bar project though has good potential, is very sensitive and seasonal and can also be a great loss for the investor.
The risk-free rate of return can be assessed at the level of about 4-6% and it can be achieved from investing into long-term government bonds and interest rate to be received from bank savings account. Authors argue that in the recent ten to fifteen years many projects were overestimated in their riskiness due to low-grade managers overestimating project profitability because they wanted to receive promotion or higher wages for initiating these projects. On the other hand, senior managers tend…