A (yearly) cash flow stream is x=(-40,10,10,10,10,10,10). The spot rates are (yearly in percentage) s=(5.0,5.3,5.6,5.8,6.0,6.1).

Use the discount factors to determine the (net) present value of the stream.

To determine the present value of the cash flow stream, we need to calculate the present value of each cash flow and sum them up.

The present value of each cash flow can be calculated using the following formula:

PV = CF / (1 + r)^n

Where PV is the present value, CF is the cash flow, r is the spot rate, and n is the year.

Let's calculate the present value of each cash flow:

PV_1 = -40 / (1 + 0.05)^1 = -40 / 1.05 = -38.10
PV_2 = 10 / (1 + 0.053)^2 = 10 / 1.107409 = 9.03
PV_3 = 10 / (1 + 0.056)^3 = 10 / 1.17718 = 8.50
PV_4 = 10 / (1 + 0.058)^4 = 10 / 1.251037 = 7.99
PV_5 = 10 / (1 + 0.06)^5 = 10 / 1.338226 = 7.48
PV_6 = 10 / (1 + 0.061)^6 = 10 / 1.427248 = 6.99
PV_7 = 10 / (1 + 0.061)^7 = 10 / 1.519344 = 6.58

Now, let's calculate the net present value (NPV) by summing up the present values of all cash flows:

NPV = PV_1 + PV_2 + PV_3 + PV_4 + PV_5 + PV_6 + PV_7
= -38.10 + 9.03 + 8.5 + 7.99 + 7.48 + 6.99 + 6.58
= $8.47

Therefore, the net present value of the cash flow stream is $8.47.

To determine the net present value (NPV) of the cash flow stream, we need to discount each cash flow to its present value and then sum them up. The formula to calculate the present value (PV) of a cash flow is:

PV = CF / (1 + r)^n

Where:
- CF is the cash flow for a specific year
- r is the interest rate (or spot rate) for the corresponding year
- n is the number of years from the present to the cash flow

To calculate the discount factors, we need to convert the spot rates into decimal form by dividing them by 100 and adding 1 to get the interest factor.

For the provided cash flow stream x = (-40, 10, 10, 10, 10, 10, 10) and spot rates s = (5.0, 5.3, 5.6, 5.8, 6.0, 6.1), let's compute the discount factors and calculate the present value of each cash flow:

Year 0: CF = -40, r = 5.0%
PV0 = -40 / (1 + 5.0% / 100)^0 = -40

Year 1: CF = 10, r = 5.3%
PV1 = 10 / (1 + 5.3% / 100)^1 = 9.48

Year 2: CF = 10, r = 5.6%
PV2 = 10 / (1 + 5.6% / 100)^2 = 8.89

Year 3: CF = 10, r = 5.8%
PV3 = 10 / (1 + 5.8% / 100)^3 = 8.31

Year 4: CF = 10, r = 6.0%
PV4 = 10 / (1 + 6.0% / 100)^4 = 7.80

Year 5: CF = 10, r = 6.1%
PV5 = 10 / (1 + 6.1% / 100)^5 = 7.33

Year 6: CF = 10, r = 6.1%
PV6 = 10 / (1 + 6.1% / 100)^6 = 6.89

Finally, we calculate the NPV by summing up all the present values:

NPV = PV0 + PV1 + PV2 + PV3 + PV4 + PV5 + PV6
= -40 + 9.48 + 8.89 + 8.31 + 7.80 + 7.33 + 6.89
= 8.70

Therefore, the net present value of the cash flow stream x is 8.70.