Economics "Dealing with Uncertainty"

PS # 4

Question 1:

a) Expected Net Benefits

E(NB) = E(B) – C

E(B) = Σ Pί . Bί

1) For Large Hospital:

E(B) = (200000x0.3) + (100000x0.5) – (120000x0.2)

= 60000 + 50000 - 24000

= 86000

E(NB) = 86000-46000 = $40000

E (NPVA)= [P1(t=zZB1(1+r)t -t=wWC1(1+r)t) +P2(t=zZB2(1+r)t -t=wWC2(1+r)t)+ (t=zZB3(1+r)t -t=wWC3(1+r)t)]

If we assume that the interest rate is 10 %, for example. So,

E (NPVA) = [0.3(t=110200000(1+0.1)t -46000) + 0.5(t=110100000(1+0.1)t -46000) + 0.2(t=110-120000(1+0.1)t -46000)]

E (NPVA) = $482,432.77

2) For Small Hospital:

E(B) = (0.3x90000) + (0.5X50000) – (0.2x20000)

= 27000 + 25000 - 4000

= 48000

E(NB) = 48000-46000 = $2000

E (NPVA)= [P1(t=zZB1(1+r)t -t=wWC1(1+r)t) +P2(t=zZB2(1+r)t -t=wWC2(1+r)t)+ (t=zZB3(1+r)t -t=wWC3(1+r)t)]

If we assume that the interest rate is 10 %, for example. So,

E (NPVA) = [0.3(t=11090000(1+0.1)t -46000) + 0.5(t=11050000(1+0.1)t -46000) + 0.2(t=110-20000(1+0.1)t -46000)]

E (NPVA) = $248,939.22

3) For No Hospital:

E(NB) = 0

E (NPVA) = 0

Variance: σ 2 = Σ P ( B1- B͡ )

Standard Deviation: σ = σ 2

Coefficient of Variation = σ 2E(NB)

Large Hospital:

σ 2Large Hospital = 0.3(200000-86000)2 + 0.5(100000-86000)2 + 0.2(-120000-86000)2

= 38988000000 + 98000000 + 84872000000

=12484000000

σ Large Hospital = 12484000000 = 111731.82

Coefficient of Variation Large Hospital = 1248400000086000 = 145162.8

Small Hospital:

σ 2Small Hospital = 0.3(90000-48000)2 + 0.5(50000-48000)2 + 0.2(-20000-48000)2

= 529200000 + 2000000 + 924800000

= 1456000000

σ Small Hospital = 1456000000 = 38157

Coefficient of Variation Small Hospital = 145600000048000 = 30333

Note: Since the cost is fixed for both alternatives, I have chosen to execlude it when calculating the Coefficient of Variation....