Question

. The Smithsonian has offered to lend SFMSA a rare collection of nineteenth century Navajo crafts. The collection would remain at the museum for a five-year period after which it would be returned. To house the exhibit, SFMSA will have to upgrade its environmental and security systems at a one-time, up-front cost of $250,000. This is the only cash outflow associated with the decision. Since this may be the last time that this collection will be exhibited in its entirety, the Executive Director is enthusiastic about the impact that it will have on visitor volume and the reputation of the museum. The Marketing Director forecasts that 1000 incremental visitors are likely to be drawn to the museum each month that the exhibit is at SFMSA. The director wants you to tell her if the exhibit is financially self-sufficient taking into account the time-value-of-money or if she will need to get a grant to support it. You know that SFMSA’s cost of capital is 5.5%. Assume the contribution margin, or net income, generated by each incremental visitor to the museum is $4.00.

Problem 3. What do you tell her based on the net present value (NPV) and internal rate of return (IRR) of the proposed collection? Can SFMSA afford to show the exhibit based solely on the marginal contribution from incremental visitors? If the exhibit is not financially self-sufficient, how large a grant will SFMSA need to get to meet the projected shortfall? (35 points)

Answer 1

Cash flows for the proposal: CF0 = -250,000; CF1 to CF5: number of incremental visitors*contribution margin = 1,000*4 = 4,000

NPV = -250,000 + 4,000[(1 -(1+5.5%)^-5)/5.5%] = -232,918.86

IRR for the given cash flows (using IRR function) = -50.10%

A grant will be required to meet the shortfall. If the grant is received at the beginning of the exhibit then it will need 232,918.86 for the exhibit to break-even. If grant is received per annum then let grant amount p.a. be g.

For NPV = 0, we have

-250,000 + (4000+G)[(1-(1+5.5%)^-5)/5.5%] = 0

(4000+G)[(1-(1+5.5%)^-5)/5.5%] = 250,000

4000 + G = 250,000/4.27028

G = 54,544.11 (grant amount per annum)